Algebraically compact rings and modules

DOI10.1007/BF01175615zbMath0363.16017MaRDI QIDQ1240291

Wolfgang Zimmermann, Birge Zimmermann Huisgen

Publication date: 1978

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/172688

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Injective modules, self-injective associative rings (16D50) Representation theory of associative rings and algebras (16Gxx)

Related Items (49)

Model theory of modules ⋮ Saturated free algebras and almost indiscernible theories ⋮ Preinjective modules and finite representation type of artinian rings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Rings whose cyclic modules are pure-injective or pure-projective ⋮ Finite matrix topologies. ⋮ Relative injectivity and pure-injective modules over Prüfer rings ⋮ Pure-direct-injective modules ⋮ Relatively Endocoherent Modules ⋮ Unnamed Item ⋮ WHEN ARE PURE-INJECTIVE ENVELOPES OF FLAT MODULES FLAT? ⋮ Indecomposable decompositions of finitely presented pure-injective modules ⋮ Rings whose Right Modules are Direct Sums of Indecomposable Modules ⋮ A Generalization of Algebraic Compactness ⋮ Modules coinvariant under the idempotent endomorphisms of their covers ⋮ Strong exchange rings ⋮ On the category vx in the preprojective partition ⋮ (Sigma-) algebraic compactness of rings ⋮ A T.T.F. theory for short exact sequences ⋮ THE ZIEGLER SPECTRUM OF THE RING OF ENTIRE COMPLEX VALUED FUNCTIONS ⋮ T.T.F. theories for left and right exact sequences ⋮ Pure-injective modules over path algebras ⋮ Endomorphism rings of completely pure-injective modules ⋮ Unnamed Item ⋮ Endoproperties of modules and local duality. ⋮ How to construct a `concrete' superdecomposable pure-injective module over a string algebra. ⋮ Endomorphism rings of modules and lattices of submodules ⋮ Sums of units in self-injective rings ⋮ Some model theory of modules. I. On total transcendence of modules ⋮ Some model theory of modules. II. on stability and categoricity of flat modules ⋮ Sigma-cotorsion rings. ⋮ Pure-injective hulls of modules over valuation rings ⋮ On the Sparsity of Representations of Rings of Pure Global Dimension Zero ⋮ On locally pure-injective modules ⋮ Strong Preinjective Partitions and Representation Type of Artinian Rings ⋮ Injective stabilization of additive functors. II. (Co)torsion and the Auslander-Gruson-Jensen functor ⋮ F-semi-perfect modules ⋮ The lattice coordinatized by a ring ⋮ Indecomposable decompositions of pure-injective modules ⋮ Model theory of modules over a serial ring ⋮ LOCALLY FINITELY GENERATED MODULES OVER RINGS WITH ENOUGH IDEMPOTENTS ⋮ Classes of modules with the exchange property ⋮ Rings of finite representation type and modules of finite Morley rank ⋮ Modules ⋮ Separativity of modules with finite exchange property ⋮ Modules invariant under automorphisms of their covers and envelopes. ⋮ Direct sums of representations as modules over their endomorphism rings ⋮ Σ-semi-compact rings and modules

Cites Work

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• Decomposability of direct products of modules
• Refinements for infinite direct decompositions of algebraic systems
• Purity and algebraic compactness for modules
• An isomorphic refinement theorem for Abelian groups
• Die Struktur von projektiven Moduln. (The structure of projective modules.)
• Direct sums of projective modules as direct summaots of their direct product
• -projektive Moduln.
• Rein injektive direkte summen von moduln
• On Continuous Rings and Self Injective Rings
• A Krull-Schmidt Theorem for Infinite Sums of Modules
• Algebraic \(K\)-theory

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