Mixed modules over ZG, G cyclic of prime order, and over related Dedekind pullbacks

DOI10.1016/0021-8693(81)90107-1zbMath0508.16009OpenAlexW2036178951MaRDI QIDQ1837750

Lawrence S. Levy

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1016/0021-8693(81)90107-1

zbMATH Keywords

finitely generated modulesprojective modulescancellationDedekind domainindecomposable modulespullback4-matrix problemseparated moduleseparated representation of modulesubdirect product of ringsZG-modules

Mathematics Subject Classification ID

Group rings (16S34) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Other classes of modules and ideals in associative algebras (16D80) Representation theory of associative rings and algebras (16Gxx)

Related Items (35)

\({\mathbb{Z}}G_ n\)-modules, \(G_ n\) cyclic of square-free order n ⋮ Classification of 1-absorbing comultiplication modules over a pullback ring ⋮ COMPUTING THE ADDITIVE STRUCTURE OF INDECOMPOSABLE MODULES OVER DEDEKIND-LIKE RINGS USING GRÖBNER BASES ⋮ On the Pure Injectivity of Certain Infinitely Generated Modules over Dedekind Pullbacks ⋮ ON SECONDARY MODULES OVER PULLBACK RINGS ⋮ Decidability for modules over a group ring - II ⋮ Unnamed Item ⋮ Three-manifolds class field theory. (Homology of coverings for a nonvirtually \(b_1\)-positive manifold) ⋮ Pseudo-absorbing comultiplication modules over a pullback ring ⋮ Almost split sequences for dedekind-like rings. II ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Higher level Zhu algebras and modules for vertex operator algebras ⋮ Pseudo-absorbing multiplication modules over a pullback ring ⋮ Commutative group rings of finite representation type ⋮ Pairs of mutually annihilating operators ⋮ THE FINITE LENGTH MODULES FOR THIN -GRADED RINGS ⋮ MODULES OVER PULL-BACKS OF ALGEBRAS ⋮ On Semiprime Multiplication Modules over Pullback Rings ⋮ On pseudo-prime multiplication modules over pullback rings ⋮ SUPERDECOMPOSABLE PURE INJECTIVE MODULES OVER COMMUTATIVE NOETHERIAN RINGS ⋮ On Prime Modules over Pullback Rings ⋮ Comultiplication modules over a pullback of Dedekind domains ⋮ Non-cyclotomic presentations of modules and prime-order automorphisms of Kirchberg algebras ⋮ The level one Zhu algebra for the Virasoro vertex operator algebra ⋮ Strongly Minimal Modules Over Group Rings ⋮ Integral representations of groups of square-free order ⋮ On 2-absorbing multiplication modules over pullback rings ⋮ Vaught's Conjecture and Group Rings ⋮ Modules over pullbacks and subdirect sums ⋮ On the krull-schmidt-azumaya theorem for integral group rings ⋮ Modules over Dedekind-like rings ⋮ On orders and multiple fibre products ⋮ On pure-injective modules over pullback rings ⋮ Sweeping-similarity of matrices

Cites Work

• Application of modules over a dyad for the classification of finite \(p\)-groups possessing an Abelian subgroup of index \(p\) and of pairs of mutually annihilating operators
• Modules over pullbacks and subdirect sums
• Lifting Isomorphisms of Modules
• Decomposability of Finitely Presented Modules
• Determination of a Certain Family of Finite Metabelian Groups
• On -Adic Integral Representations of Finite Groups
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