Summands of Separable Abelian Groups: Dedicated to Paul Turán on his 60th Birthday

DOI10.1112/blms/2.2.205zbMath0213.03501OpenAlexW2015697739WikidataQ122150426 ScholiaQ122150426MaRDI QIDQ5614695

László Fuchs

Publication date: 1970

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/blms/2.2.205

Mathematics Subject Classification ID

Direct sums, direct products, etc. for abelian groups (20K25)

Related Items

A characterization of sets containing absolutely nonmeasurable subsets ⋮ D4-Modules ⋮ On the socles of characteristically inert subgroups of abelian \(p\)-groups ⋮ Abelian p-groups with minimal characteristic inertia ⋮ Pure Subgroups of Torsion-Free Groups ⋮ A torsion-free abelian group of finite rank exists whose quotient group modulo the square subgroup is not a nil-group ⋮ On transitivity-like properties for torsion-free abelian groups ⋮ Weakly locally compact abelian groups and their basic properties ⋮ Modules and abelian groups with a bounded domain of injectivity ⋮ Torsion-free abelian groups with optimal Scott families ⋮ On hereditarily and super R-Hopfian and L-co-Hopfian abelian groups ⋮ Quotient-transitivity and cyclic subgroup-transitivity ⋮ Lie groups as permutation groups: Ulam's problem in the nilpotent case ⋮ Finite Σ-Rickart modules ⋮ K-theoretic duality for hyperbolic dynamical systems ⋮ Abelian groups with \(\pi\)-regular center of the endomorphism ring ⋮ THE COMPLEXITY OF THE EMBEDDABILITY RELATION BETWEEN TORSION-FREE ABELIAN GROUPS OF UNCOUNTABLE SIZE ⋮ Big lattices of module classes induced by preradicals ⋮ Weakly fully and characteristically inert socle-regular Abelian p-groups ⋮ On the full transitivity of a cotorsion hull ⋮ Different characterizations of large submodules of QTAG-modules ⋮ Modules and abelian groups with minimal (pure-) projectivity domains ⋮ A Friedberg enumeration of equivalence structures ⋮ On abelian groups having isomorphic proper strongly invariant subgroups ⋮ On the question of definability of homogeneously decomposable torsion-free abelian groups by their homomorphism groups and endomorphism rings ⋮ MEASURING DEPENDENCE IN METRIC ABSTRACT ELEMENTARY CLASSES WITH PERTURBATIONS ⋮ On the Square Subgroup of a MixedSI-Group ⋮ On closed subgroups of precompact groups ⋮ Abelian groups whose nonzero endomorphisms have nonessential kernels ⋮ The dual Schröder-Bernstein problem for modules ⋮ On the weak-injectivity profile of a ring ⋮ On simple-direct modules ⋮ The upper central series of the maximal normal \(p\)-subgroup of a group of automorphisms ⋮ On the supremum of the pseudocompact group topologies ⋮ On the residue fields of Henselian valued stable fields ⋮ Characterizing categorically closed commutative semigroups ⋮ ABELIAN GROUPS WITH LEFT COMORPHIC ENDOMORPHISM RINGS ⋮ Characterizations of democratic systems of translates on locally compact abelian groups ⋮ On the lattice of cotorsion theories ⋮ Unnamed Item ⋮ Torsion Free Groups ⋮ Abelian groups ⋮ Corrections to A completion functor on modules and algebras ⋮ Abelian groups admitting a Fréchet-Urysohn pseudocompact topological group topology ⋮ Cross sections and homeomorphism classes of Abelian groups equipped with the Bohr topology ⋮ Generalized pure modules ⋮ An extension of expectation ⋮ Consistency of random field specifications ⋮ Relating properties of a ring and its ring of row and column finite matrices ⋮ On commutator Krylov transitive and commutator weakly transitive abelian \(p\)-groups ⋮ Algebraic structure of countably compact non-torsion abelian groups of size continuum from selective ultrafilters ⋮ Borel equivalence relations and classifications of countable models ⋮ On a problem of Călugăreanu, Chekhlov and Krylov regarding pure endomorphic images of abelian groups ⋮ Mixed Groups ⋮ On orbits without the Baire property ⋮ Selmer groups are intersection of two direct summands of the adelic cohomology ⋮ An analogue of the Wielandt subgroup in infinite groups ⋮ Polish topologies for graph products of groups ⋮ Groups whose proper subgroups are linear ⋮ Hereditarily minimal topological groups ⋮ On the structure of some locally nilpotent groups without contranormal subgroups ⋮ Two problems of Fuchs concerning tor and hom ⋮ Minimality for actions of abelian semigroups on compact spaces with a free interval ⋮ On additive groups of associative and commutative rings ⋮ The rotation class of a flow ⋮ Associates, irreducibility, and factorization length in monoid rings with zero divisors ⋮ Finite factorization properties in commutative monoid rings with zero divisors ⋮ Quotient-transitivity and cyclic submodule-transitivity for p-adic modules ⋮ An addendum to the Vietoris-Begle theorem ⋮ The model theory of unitriangular groups ⋮ The linking homomorphism of one-dimensional minimal sets ⋮ Real spectra of quantum groups ⋮ Valuation domains without pathological modules ⋮ Group representations and construction of minimal topological groups ⋮ Locally compact abelian groups admitting non-trivial quasi-convex null sequences ⋮ Totally Crawley groups ⋮ Unit groups of semisimple group algebras of Abelian \(p\)-groups over a field ⋮ Cellular covers of groups ⋮ A characterization of \(\aleph _ 1\)-free Abelian groups and its application to the Chase radical ⋮ Produits lexicographiques de groupes ordonnés: Isomorphisme et équivalence élémentaire. (Lexicographic products of ordered groups: isomorphism and elementary equivalence) ⋮ Revisiting the free 2-generator abelian \(\ell\)-group ⋮ On the model theory of the ring \(\mathrm{NT}(n,R)\) ⋮ Closure operators and functorial topologies ⋮ Groups without faithful transitive permutation representations of small degree ⋮ Linear groups rich in finite quotients ⋮ Subvariety structures in certain product varieties of groups ⋮ Subgroups generated by images of endomorphisms of abelian groups and duality ⋮ Normal \(p\)-subgroups of the automorphism group of an Abelian \(p\)-group ⋮ On strong homology of compact spaces ⋮ Cardinal invariants and independence results in the poset of precompact group topologies ⋮ László Fuchs' 70th birthday ⋮ Cotorsion and wild homology ⋮ Über Torsions-und \(\kappa\)-Elemente von Ext(C,A) ⋮ Supertropical quadratic forms. I. ⋮ Some model theory for Henselian valued fields ⋮ The endomorphism ring of homogeneously decomposable separable groups ⋮ Abelian extensions of topological vector groups ⋮ A characterization of the circle group via uniqueness of roots ⋮ Torsion and divisibility in finitely generated commutative semirings ⋮ Outer automorphisms of locally finite \(p\)-groups. ⋮ The classification problem for \(S\)-local torsion-free abelian groups of finite rank ⋮ A sufficient condition for separability ⋮ Finite groups of automorphisms of infinite groups. I ⋮ On Bousfield's problem for solvable groups of finite Prüfer rank ⋮ Finite automata presentable Abelian groups ⋮ Filtration-equivalent \(\aleph_1\)-separable Abelian groups of cardinality \(\aleph_1\). ⋮ Groups elementarily equivalent to a free nilpotent group of finite rank ⋮ Lösung eines Problems von L. Fuchs ⋮ Pluri-adjoints and preservation of finite limits ⋮ On pure-projective modules over Artin algebras ⋮ Tight subgroups in torsion-free Abelian groups. ⋮ A method for solving a conditional Cauchy equation on Abelian groups ⋮ Enumerations of rooted trees with an application to group presentations ⋮ p-adic and p-cotorsion completions of nilpotent groups ⋮ On injective hulls of simple modules ⋮ On the splitting group basis problem for Abelian group rings ⋮ On the Reidemeister spectrum of an abelian group ⋮ Linear compactness and Morita duality for Grothendieck categories ⋮ Free \(\sigma\)-products and noncommutatively slender groups ⋮ Long chains of topological group topologies. --- A continuation ⋮ Some aspects of \((\omega +1)\)-projectives ⋮ Characterizing Lie groups by controlling their zero-dimensional subgroups ⋮ The impact of Pontryagin and Bohr functors on large-scale properties of locally compact abelian groups ⋮ On strongly just infinite profinite branch groups ⋮ On projectively Krylov transitive and projectively weakly transitive abelian \(p\)-groups ⋮ On products of primary abelian groups ⋮ The Heyde theorem for locally compact abelian groups ⋮ Forcing hereditarily separable compact-like group topologies on Abelian groups ⋮ On stout and slender groups ⋮ Abelian 1-factorizations in infinite graphs ⋮ Vector spaces with valuations ⋮ An application of B-high subgroups of abelian p-groups ⋮ Stabilizers of direct composition series. ⋮ Endomorphisms of abelian groups and the theorem of Baer and Kaplansky ⋮ On spectral analysis and spectral synthesis in the space of tempered functions on discrete abelian groups ⋮ Rings of pure global dimension zero and Mittag-Leffler modules ⋮ Tensor products of mixed Abelian groups ⋮ On the global dimension of the functor category (mod R, Ab) ⋮ On constructing indecomposable groups in L ⋮ Localizations of endomorphism rings and fixpoints ⋮ p-coprimary functors with enough projectives ⋮ On thickness and decomposability of abelian \(p\)-groups ⋮ The endomorphism ring of pointed separable torsion-free Abelian groups ⋮ Decomposability of direct products of modules ⋮ Locally finite near fields ⋮ Boolean powers of abelian groups ⋮ On the summand theorem for A-groups ⋮ Effective categoricity of abelian \(p\)-groups ⋮ Groups with the weak minimal condition for non-subnormal subgroups ⋮ A generalized direct product of Abelian groups ⋮ E-transitive torsion-free Abelian groups ⋮ Representative functions on discrete solvable groups ⋮ Varieties for modules and a problem of Steenrod ⋮ The existence of certain pure dense subgroups of Abelian p-groups is not decidable in ZFC ⋮ On groups of finite Morley rank with weakly embedded subgroups ⋮ On the global dimension of the functor category \(((\bmod R)^{op},Ab)\) and a theorem of Kulikov ⋮ Purity and injectivity in accessible categories ⋮ Separable torsion-free Abelian \(E^*\)-groups ⋮ Torsion-free Abelian groups with isomorphic endomorphism rings ⋮ Classes of modules with the exchange property ⋮ On the endomorphic images of \(C_{\lambda}\)-groups ⋮ Exact embedding functors for module categories and submodule lattice quasivarieties ⋮ Locally factorial integral domains ⋮ The torsion group of a field defined by radicals ⋮ A note on endomorphisms of hypercentral groups ⋮ Minimal and precompact group topologies on free groups ⋮ Countable algebra and set existence axioms ⋮ Knot groups whose bases are abelian