Associative rings

DOI10.1007/BF01093433zbMath0621.16001OpenAlexW4211247117MaRDI QIDQ5903401

Alexander V. Mikhalev, Viktor T. Markov, Kostia I. Beidar, Askar A. Tuganbaev, Victor N. Latyshev, Leo Anatolevich Skornyakov

Publication date: 1987

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01093433

zbMATH Keywords

surveyBibliographyassociative rings

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02) Associative rings and algebras (16-XX)

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• Automorphismes algebriques
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• On M-nilpotent rings
• On Tensor Products and Extended Centroids
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• Quasi-ideals and bi-ideals in radical theory
• A topology on the class of unequivocal rings
• Fixed Subalgebra of a Frobenius Algebra
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• Weakly homomorphically closed semisimple classes
• Primes in algebras and the arithmetic in central simple algebras
• Strong crossed product division algebras^∗
• Stable Rings
• On regular semigroups, semirings and rings
• Affine representations of Grothendieck groups and applications to Rickart 𝐶*-algebras and ℵ₀-continuous regular rings
• Rings of small order
• Bounded number of generators of right ideals in polynomial rings
• On Derivations in Prime Rings and a Question of Herstein
• Observations on crossed products and fixed rings
• Radicals of rings and subrings
• Equivalent conditions for cancellation of graded azumaya algebras
• Regular rings and distributive lattices
• The polynomial identities of matrices in characteristic zero
• On Making Rings Weakly Finite
• Solvable Groups of Unipotent Elements in a Ring
• Divisible Ideals of Noetherian Rings
• K -Symmetric Rings
• Semicentralizing automorphisms of prime rings
• Prime Quantifier Eliminable Rings
• Arithmetical and semihereditary semigroup rings
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• Essentially closed classes of rings and upper radicals
• On a Theorem From "Skew Field Constructions"
• Prime Ideals in Intermediate Extensions
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• Quasi-ideals in rings
• Regular Rings are Very Regular
• Localization in pi-rings
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• Injectives for ring monomorphisms with accessible images
• Rigid Artinian rings
• The Extended Center of Coproducts
• Regularity of Zero Divisors
• Homogeneous direct summands of regular rings of finite index
• Normal Classes of Prime Rings Determined by Modules
• Central closure of semiprime tensor products
• Absolute retracts, relatively injective simple objects and Brown-McCoy radicals
• Von neuman finiteness of tensor products of algebras
• Rings of Sets Are Really Rings
• A Negative Answer to Three Questions on K-Primitive Rings
• Galoiserweiterungen von night-kommutativen ringen
• A Free Algebra can Be Free as a Module over a Nonfree Subalgebra
• Krull Dimension and Reflexivity in some Noetherian Rings
• Decomposition of Maximal orders
• Solvable Subgroups in Prime Rings
• Dihedral Algebras are Cyclic
• Actions de groupes et traces
• Jacobson radicals and maximal ideals of normalizing extensions applied toZ-graded rings
• A jacobian conjecture for free associative algebras
• The radical in a finitely generated P. I. algebra
• Metrically Complete Regular Rings
• A Theorem on Derivations of Prime Rings with Involution
• Anneaux fidelement representes sur leur socle droit
• Finite Dimensional Right Duo Algebras are Duo
• On Semiprime Rings of Bounded Index
• Skew polynomials and brown-mccoy rings
• The Nullstellensatz and Jacobson Properties for Rings of Differential Operators
• Sur les anneaux simples différentiels
• On the Lattice of Subalgebras of an Algebra
• On radicals of finitely generated algebras
• Some examples of finitely generated algebras
• The robson cubics generate all polyhomials satisfied by the general 2× 2 matrix
• Nilpotence and normalizing extensions
• Derivations of prime rings having power central values
• A chain of Kurosh may have an arbitrary finite length
• Rings with Bounded Index of Nilpotence
• Fonction de Hilbert-Samuel dans les anneaux locaux réguliers non-commutatifs
• The polynomial identities of matrices
• On the Gel′fand-Kirillov dimension of Noetherian P.I.-algebras
• A simple proof of Kostant’s theorem, and an analogue for the symplectic involution
• On the Jacobson density theorem
• Lie and Jordan Mappings
• On semigroups of endomorphisms of generalized Boolean rings
• On Jordan Structure in Semiprime Rings
• An embedding theorem for rings
• The jacobson radical and fixed rings of automorphisms
• Lie and Jordan Ideals in Prime Rings with Derivations
• A note on semiprimitivity of ore extensions
• Anneaux semi-premiers, noethériens, à identités polynômiales
• Commutativity of Rings with Abelian or Solvable Units
• An Analog of Nagata's Theorem for Modular LCM Domains
• Azumaya algebras and rings with polynomial identity (Addendum)
• On the Krull-Akizuki Theorem
• The Finite Intersection Property on Annihilator Right Ideals
• Radicals and functional representations
• Algebras with a Diagonable Subspace whose Centralizer Satisfies a Polynomial Identity
• A Note on Subnormal Subgroups of Division Algebras
• Rings in which every proper right ideal is maximal
• On the subalgebras of certain finitely presented algebras
• Special closure,M-radicals, and relative complements
• Centralizing Automorphisms of Prime Rings
• Über die Struktur galoisscher Erweiterungen einfacher Ringe.
• On a Central Identity for Matrix Rings
• The Unity in Rings with Gabriel and Krull Dimension
• On Rings with Many Endomorphisms
• Local Rings with Elementary Abelian Units
• The invariants of 𝑛×𝑛 matrices
• Multiplicatively Periodic Rings
• Commutative subrings of periodic rings.
• Idempotent Ideals in P.I. Rings
• Primitive Ore extensions
• Left and right invariance in an integral domain
• Prime 𝑃𝐼-rings
• Abstract
• On Subgroups of the Multiplicative Group of Skew Fields
• Must r be noetherian if r^Gis noetherian
• Dedekind k-subalgebras of k(x)
• Normal radicals
• Simple Going Down in PI Rings
• On the transfer of properties to subidealizer rings
• A Note on a Class of Simple Noetherian Domains
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• A skew polynomial ring over a jacobson ring need not be a jacobson ring
• Algebraically closed noncommutative polynomial rings
• Representing Rank Complete Continuous Rings
• The real closure of a commutative regular f-ring
• Noetherian Rings with Krull Dimension One
• A Generalization of the Artin-Procesi Theorem
• Über den vertauschungsring von permutationsgruppen
• Commutative rings in which every proper ideal is maximal
• Radical Pairs
• Central simple algebras with involution
• Completions of Rank Rings
• On modular right ideals of a ring
• Reflexive Ideals in Simple Ore Extensions
• Indecomposable Decompositions and the Minimal Direct Summand Containing the Nilpotents
• Über endliche galoissche schiefkörpererweiterungen ohne endliche galoisgruppen
• General hereditary for radical theory
• Coordination Applied to Finite Baer ∗ Rings
• Affine 𝑃𝐼 rings are catenary
• Primitive skew Laurent polynomial rings
• Non-cummutative minimally non-Noetherian rings.
• An Uncountable Noetherian Ring with Free Additive Group
• An analogue of the pierce sheaf for non-commutative rings
• On the Nonexistence of Hypercommuting Polynomials
• Finite Principal Ideal Rings
• Does Every Right Ideal of a Matrix Ring Contain a Nilpotent Element?
• On filters generated by sequences of ideals
• Fixed Rings of Automorphisms and the Jacobson Radical
• Tensor Products of Division Rings and Finite Generation of Subfields
• A generalization of a theorem of A. Kertész
• On Semicommuting Automorphisms of Rings
• Ideals inZ[x, y]
• Instabilité Des Corps Formellement Réels
• Fragmented rings
• A Theorem for Prime Rings
• The Normal Basis Theorem for Skew Field Extensions
• Fixed rings of simple rings
• When is the unit group of a dedekind order solvable?
• Free Subgroups of Normal Subgroups of the Multiplicative Group of Skew Fields
• Shorter Notes: A Short Proof of the Dawkins-Halperin Theorem
• Outer Automorphisms of Semi-Prime Rings
• Über ARTINsche Ringe
• Herstein's conjecture, automorphisms and the schur group
• Constructing a ring without unique factorisation
• Rigid Rings
• On a Result of Levitzki
• The hulls of semiprime rings
• On the Commutativity of Semi-Simple Associative Algebras
• Anneaux de polynomes de ore sur des anneaux artiniens
• Centralizers and Multilinear Polynomials in Non-Commutative Rings
• Centralizers of algebraic elements
• On the multiplicative semigroups of rings
• Ideals contracted from each extension ring
• Ringe mit dichtem Rechtsquasizentrum
• Lattices of radicals for heredita rily ARTINian rings
• Fully idempotent factorization rings
• Unique factorization in rings with right ACC₁
• Skew polynomial rings and skew power series rings
• A Version of Zariski's Main Theorem for Polynomial Identity Rings
• Some factorable nil rings of characteristic two
• A Characterization of Prime Noetherian P.I. Rings and a Theorem of Mori- Nagata
• Going down and the spec map in pi rings
• Rings all of Whose Pierce Stalks are Local
• T -Ideals of Degree 3 are Finitely Generated
• Artinian Skew Group Rings
• A Note on Derivations
• Order completions of semiprime rings
• Characterizing and constructing special radicals
• Affine rings satisfying a polynomial identity
• Division algebras. A survey
• Idempotents and completely semiprime ideals
• On Automorphisms of Polynomial Rings
• Principal Ideal Rings and Separability
• Automorphismes algebriques et algebre du grouse
• Ω-krull rings. I
• THE THEOREM AßOUT INVERSION IN THE GENERALIZED INCIDENCE ALGEBRA
• Rings with Enough Invertible Ideals
• RINGS WITH A BOUNDED NUMBER OF GENERATORS FOR RIGHT IDEALS
• Varieties of Rings with Definable Principal Congruences
• Torsion-free rings with almost regular automorphisms
• A Condition for a Ring to be Boolean
• Locally Finite and Solvable Subgroups of Sfields
• Axioms for Boolean rings
• The Categories of p-Rings are Equivalent
• The semigroup of endomorphisms of a Boolean ring
• Embedding Rational Division Algebras
• Injective Objects in the Category of p-Rings
• On (von Neumann) regular rings
• Boolean Rings of Sets with Finite Subcovering Property
• Algebraically Closed Regular Rings
• Endomorphism rings of modules and lattices of submodules
• Division algebras of degree 4 and 8 with involution
• Generalized rational identities and rings with involution
• On a theorem of herstein and small
• Generic algebras
• Krull Dimension of Differential Operator Rings
• Endomorphism rings of modules and lattices of submodules
• Varieties of associative algebras