Bjarni Jónsson's contributions in algebra

DOI10.1007/BF01221790zbMath0806.08001OpenAlexW2033242129MaRDI QIDQ1327458

Kirby A. Baker

Publication date: 18 July 1994

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01221790

zbMATH Keywords

varietiesrelational structurescongruence distributivity

Mathematics Subject Classification ID

Biographies, obituaries, personalia, bibliographies (01A70) Development of contemporary mathematics (01A65) Congruence modularity, congruence distributivity (08B10) Relational systems, laws of composition (08A02) History of general algebraic systems (08-03)

Related Items (2)

Bjarni Jónsson's contributions in algebra: an addendum ⋮ Tribute to Bjarni Jónsson

Cites Work

• Homogeneous Universal Models.
• Models of complete theories
• The Variety of Modular Lattices is Not Generated by its Finite Members
• Global subdirect products
• A Concrete Representation Theorem for Intervals of Multirelations
• The lattice of modal logics: an algebraic investigation
• Join algebras
• Stability theory and Algebra
• Two model theoretic ideas in independence proofs
• Homogeneous Universal Models of Universal Theories
• Implikative BCK‐Algebren
• DIE ENDLICHEN, SUBDIREKT IRREDUZIBLEN ELEMENTE DER VARIETÄT DER BESCHRÄNKTEN KOMMUTATIVEN BCK‐ALGEBREN
• Ultrahomogeneous Structures
• A representation theory for the variety generated by the triangle
• Boolean powers of groups
• Primitive Satisfaction and Equational Problems for Lattices and Other Algebras
• Primitive Elements and One Relation Algebras
• On Malcev conditions
• The Amalgamation Property, the Universal-Homogeneous Models, and the Generic Models.
• Unique reducibility of subsets of commutative topological groups and semigroups.
• Equational Bases for Lattice Theories.
• Second order forcing, algebraically closed structures, and large cardinals
• On the Triple Characterization for Stone Algebras
• Dualities for Equational Classes of Brouwerian Algebras and Heyting Algebras
• Pure Compactifications in Quasi-Primal Varieties
• Weak Injectivity and Congruence Extension in Congruence-Distributive Equational Classes
• The structure of modular lattices of width four with applications to varieties of lattices
• A selection theorem for Boolean correspondences.
• Zur Konstruktion vollständiger Polaritätsverbände.
• On modules over rings of type (n, k)
• Complete Universal Locally Finite Groups
• Exponents of Finite Simple Lattices
• Universal horn classes categorical or free in power
• An undecidability result for relation algebras
• Model theory for universal classes with the amalgamation property: A study in the foundations of model theory and algebra
• A model theoretic approach to Malcev conditions
• Equational Theories of Algebras with Distributive Congruences
• Closed Hulls in Infinite Symmetric Groups
• Varieties of Orthomodular Lattices
• Varieties of Orthomodular Lattices. II
• On endomorphism structure for algebras over a fixed set
• Cylindric-relativised set algebras have strong amalgamation
• Varieties of modular p-algebras
• Spaces Homeomorphic to (2 a ) a . II
• Axiom systems for first order logic with finitely many variables
• On a problem of Sikorski in the set representability of Boolean algebras
• Direct Products and Sums of Torsion-Free Abelian Groups
• Algebraic semantics for quasi-classical modal logics
• Countable Homogeneous Tournaments
• A Class of Torsion-Free Abelian Groups of Finite Rank
• Algebra valued functors in general and tensor products in particular
• Three examples on hopficity in torsion-free abelian groups
• A Note on Universal Homogeneous Models.
• Varieties of groups
• Categoricity in Power
• On the Existence of Rigid Compact Ordered Spaces
• Finite inseparability of some theories of cylindrification algebras
• A Characterization of Modularity for Congruence Lattices of Algebras*
• Completions of B<scp>OOLEAN</scp> Algebras with operators
• An Almost Everywhere Direct Power
• On Cancellation in Groups
• Some properties of completely decomposable torsion free Abelian groups
• ÜBER EINE VERALLGEMEINERUNG DER ROBINSONSCHEN MODELLVERVOLLSTÄNDIGUNG I
• Remarks on abstract algebras having bases with different number of elements
• Independence in abstract algebras results and problems
• Two Mal'cev-type theorems in universal algebra
• Direct sums in general algebra
• On Equational Classes of Algebraic Versions of Logic I.
• Equational axioms for classes of lattices
• The automorphisms groups of symmetric algebras
• Injectivity in model theory
• Remarks on Some Theorems of Rado on Universal Graphs
• The Stone Space of the Saturated Boolean Algebras
• Homogeneous Universal Modules.
• Semantic analysis of tense logics
• \(2^{\aleph_0}\) varieties of Heyting algebras not generated by their finite members
• An application of Whitman's condition to lattices with no infinite chains
• Zero-divisors among finite structures of a fixed type
• Base-undecidable properties of universal varieties
• Finite equational bases for finite algebras in a congruence-distributive equational class
• The algebraic closure of a function
• Near unanimity identities and congruence distributivity in equational classes
• Para primal algebras
• Homogeneity conditions in graphs
• Baker's finite basis theorem
• Filtered products of congruences
• Para primal varieties: A study of finite axiomatizability and definable principal congruences in locally finite varieties
• Some sufficient conditions for the representability of relation algebras
• Characterizations of arithmetical varieties
• Totally categorical groups and rings
• Injectivity and Boolean powers
• Lattice conditions implying congruence modularity
• Congruence-distributive polynomial reducts of lattices
• Congruence lattices of powers of an algebra
• Identities satisfied by a finite ring
• Varieties having Boolean factor congruences
• The ascending varietal chain of a variety of semigroups
• Undecidability of Brouwerian semilattices
• Covering in the lattice of equational theories and some properties of term finite theories
• Note on congruences of a direct product of algebras
• On the structure of varieties with equationally definable principal congruences. I
• A nonassociative extension of the class of distributive lattices
• Torsion-free extensions of torsion-free abelian groups
• Congruence lattices of semilattices
• Covering relations among lattice varieties
• A proof of Baker's finite-base theorem on equational classes generated by finite elements of congruence distributive varieties
• A method for obtaining refinement theorems, with an application to direct products of semigroups
• The congruence extension property and subdirectly irreducible algebras - an example
• Automorphism and subalgebra structure in algebras of finite type
• S-verklebte Summen von Verbänden
• On modular lattices with four generators
• On the number of homogeneous models of a given power
• Isomorphism invariants for Abelian groups modulo bounded groups
• Some model theoretic results for \(\omega\)-logic
• Universal homogeneous Boolean algebras
• Equational classes of modular lattices
• On the fundamental subdirect facorization theorems of primal algebra theory
• The lattice of equational classes of idempotent semigroups
• Algebraic and equational semi-maximality; equational spectra. II
• An isomorphic refinement theorem for Abelian groups
• Die primitiven Klassen arithmetischer Ringe
• Injectives in non-distributive equational classes of lattices are trivial
• Abelian groups which admit only nilpotent multiplications
• Extending Boolean operations
• Rechtskomplementäre Halbgruppen. Axiome, Polynome, Kongruenzen. (Right- complementary semigroups. Axioms, polynomials, congruences)
• Completions of Boolean algebras with partially additive operators
• A note on the join and subdirect product of equational classes
• Equational classes generated by finite algebras
• Amalgamation, congruence-extension, and interpolation properties in algebras
• Universal homogeneous algebras
• Implication algebras are 3-permutable and 3-distributive
• Note on direct decompositions of torsion-free abelian groups
• Varieties of implicative semilattices
• Completeness in arithmetical algebras
• On countable n-valued Post algebras
• Large superuniversal metric spaces
• The classification of certain classes of torsion free Abelian groups
• Fixed points of endomorphisms
• Residually small varieties
• The amalgamation property in equational classes of modular lattices
• Varieties of implicative semi-lattices. II
• On primal algebras
• Notes on combinatorial set theory
• Primitive subsets of lattices
• A generalization of Stone's representation theorem for Boolean algebras
• Identical relations in finite groups
• Varieties of complex algebras
• The representation of relational algebras
• Some Aspects of the Theory of Models
• On some fundamental problems concerning isomorphism of Boolean algebras
• Properties preserved under algebraic constructions
• Cylindric and Polyadic Algebras
• Nonmodular lattice varieties
• Equationally Complete Discriminator Varieties of Groupoids
• Geometrical methods in congruence modular algebras
• A Stone Type Representation Theorem for Algebras of Relations of Higher Rank
• Finite Basis Theorems for Relatively Congruence-Distributive Quasivarieties
• Amalgamation for Inverse and Generalized Inverse Semigroups
• The structure of algebraically and existentially closed Stone and double Stone algebras
• MODAL COMPANIONS OF SUPERINTUITIONISTIC LOGICS: SYNTAX, SEMANTICS, AND PRESERVATION THEOREMS
• Some Varieties Containing Relation Algebras
• On the Universal Theory of Classes of Finite Models
• Galois Theory for Cylindric Algebras and its Applications
• A Cancellation Criterion for Finite-Rank Torsion-Free Abelian Groups
• ALGEBRAISCHE CHARAKTERISIERUNGEN PRÄPRIMALER ALGEBREN
• Distributive Lattices with a Dual Endomorphism
• Universal Locally Finite Central Extensions of Groups
• The equational classes generated by single functionally precomplete algebras
• Groups Acting on Infinite Dimensional Projective Spaces
• Semi-de Morgan algebras
• The Fraser-Horn and Apple Properties
• Lattice varieties covering \(V(L_ 1)\)
• Finite fixed point algebras are subdiagonalisable
• Strong amalgamation of distributive lattices
• A duality for Boolean algebras with operators
• Counting models in universal Horn classes
• Der Verband der normalen verzweigten Modallogiken
• Algebras in permutable varieties: Geometrical properties of affine algebras
• The structure of countable Boolean algebras
• Congruence-lattices of discrete RUCS varieties
• The representation of relation algebras. II
• Properties preserved under homomorphism
• Connections between congruence-lattices and polynomial properties
• Nondefinability of projectivity in lattice varieties
• Varieties of lattice-ordered algebras
• A compact space with a measure that knows which sets are homeomorphic
• On subdirectly irreducible lattice-ordered semigroups
• Aspects of distributivity
• On congruence n-distributivity of ordered algebras
• On Jónsson's theorem
• Splitting p-algebras
• Combinatorial aspects of relations
• A portrait of Alfred Tarski
• Congruence distributive quasivarieties whose finitely subdirectly irreducible members form a universal class
• Bounded and well-placed theories in the lattice of equational theories
• Collapsed toposes and cartesian closed varieties
• Demi-pseudocomplemented lattices: Principal congruences and subdirect irreducibility
• Categoricity of theories in \(L_{\kappa \omega}\), with \(\kappa\) a compact cardinal
• Modular subalgebra lattices
• Interpolation property for extensions of intuitionistic provability logic
• Equations not preserved by complete extensions
• Lattices of width three generate a nonfinitely based variety
• On residual varieties of groups
• Endomorphisms and homomorphisms of Heyting algebras
• Amalgamation classes of some distributive varieties
• Relation algebras: Concept of points and representability
• Products of lattice varieties
• Almost distributive lattice varieties
• When is a variety a topos ?
• Elementary and algebraic properties of the Arens-Kaplansky constructions
• Finitely determined arithmetical varieties need not be universally- finite
• A property of the lattice of equational theories
• Varieties of groupoids with comprehensive free products
• Cofinality of algebras
• Every idempotent plain algebra generates a minimal variety
• Semi-local localizations of rings and subdirect decompositions of modules
• Topology and duality in modal logic
• Finite equational bases for congruence modular varieties
• Errata to ``An alternative construction of Conway's ordered field No.
• A note on Jónsson's theorem
• Torsion-free Abelian groups of finite rank without nilpotent endomorphisms
• On the structure of subalgebra systems of idempotent entropic algebras
• The decision problem for finite algebras from arithmetical varieties with equationally definable principal congruences
• An abstract theory of invertible relations
• Reduced sub-powers and the decision problem for finite algebras in arithmetical varieties
• Minimal, locally-finite varieties that are not finitely axiomatizable
• Symmetries of directed graphs and the chinese remainder theorem
• Uniform congruence schemes
• Every finite lattice can be embedded in a finite partition lattice
• Injectivity and congruence extension property in congruence distributive equational classes
• Laws in finite loops
• Algebras with minimal spectrum
• Order relations on symmetric semigroups of transformations and on their homomorphic images
• A proof of Lyndon's finite basis theorem
• Simple algebras and multiplicity types
• Remarks on Boolean products
• Elementary properties of free extensions
• The lattice of varieties of modal algebras is not strongly atomic
• Boolean modules
• Congruence modularity is permutability composed with distributivity
• Very strongly rigid Boolean algebras, continuum discrete set condition, countable antichain condition. I
• The number of subdirectly irreducible algebras in a variety. II
• A variety generated by a finite algebra with \(2^{\aleph_0}\) subvarieties
• Some applications of the term condition
• Cancellation of modules and groups and stable range of endomorphism rings
• Structural diversity in the lattice of equational theories
• Varieties with \(n\)-principal compact congruences
• Programs as partial graphs. I: Flow equivalence and correctness
• The number of non-isomorphic denumerable models of certain universal Horn classes
• Exponents of lattice-ordered algebras
• Duality and invariants for Butler groups
• Local quasi-isomorphisms of torsion free Abelian groups
• Weakly associative lattices with congruence extension property
• Algebras with modular lattice reducts and simple subdirectly irreducibles
• Algebraic closure operators and strong amalgamation bases
• Varieties whose congruences satisfy certain lattice identities
• Equationally semi-complete varieties
• Characterizing Mal'cev conditions
• Progress in free associative algebras
• Primality and model-completions
• Power-cancellation of groups and modules
• Amalgamation properties and interpolation theorems for equational theories
• Splitting algebras and a weak notion of projectivity
• The spectrum of an equational class of groupoids
• Boolean powers
• The fine spectrum of a variety
• Relatively free implicative semi-lattices
• Mal'cev varieties
• The number of subdirectly irreducible algebras in a variety
• Intervals in the lattice of varieties
• Equational axioms for classes of Heyting algebras
• A sufficient condition for a variety to have the amalgamation property
• A note on varieties of unary algebras
• Equational Classes of Distributive Pseudo-Complemented Lattices
• The Structure of Pseudocomplemented Distributive Lattices. I: Subdirect Decomposition
• The Structure of Pseudocomplemented Distributive Lattices. II: Congruence Extension and Amalgamation
• The Amalgamation Property for G-Metric Spaces
• Regular Identities in Lattices
• Varieties generated by modular lattices of width four
• Automorphism Groups of Algebras of Finite Type
• Extending Congruence Relations
• Injectivity in Equational Classes of Algebras
• Local Malcev Conditions
• Diagrammatic Construction of Homogeneous Universal Models
• Universal algebras with all operations of bounded range
• Countable homogeneous relational structures and ℵ₀-categorical theories
• Adequate Ultrafilters of Special Boolean Algebras
• Primitive Klassen von modularen S-Algebren.
• A Sheaf-Theoretic Duality Theory for Cylindric Algebras
• Cylindric Algebras and Algebras of Substitutions
• Equational Bases and Nonmodular Lattice Varieties
• Distributivity and Permutability of Congruence Relations in Equational Classes of Algebras
• Direct Decompositions Into Infinitely Many Summands
• A note on the unique factorization of abstract algebras
• A Factoring Theorem for Homomorphisms
• Identities in Two-Valued Calculi
• Duality for groups
• Some Interconnections Between Modern Algebra and Mathematical Logic
• Identities in Finite Algebras
• On the distributivity of a lattice of lattice-congruences
• Products of absolute retracts
• A family of countable homogeneous graphs
• Demi-semi-primal algebras and Mal'cev-type conditions
• 3-3 lattice inclusions imply congruence modularity
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