Rings whose finitely generated modules are direct sums of cyclics

DOI10.1016/0021-8693(74)90178-1zbMath0286.13006OpenAlexW2001171889MaRDI QIDQ1845915

Roger Wiegand, Thomas S. Shores

Publication date: 1974

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

Full work available at URL: https://doi.org/10.1016/0021-8693(74)90178-1

Mathematics Subject Classification ID

Structure, classification theorems for modules and ideals in commutative rings (13C05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (25)

Unnamed Item ⋮ Idealization of a module ⋮ CF-modules over commutative rings ⋮ The canonical form of multiplication modules ⋮ Invertible bases and root vectors for analytic matrix-valued functions ⋮ Divisibility theory in commutative rings: Bézout monoids ⋮ A characterization of FGC rings. ⋮ Prime uniserial modules and rings ⋮ A general theory of structure spaces with applications to spaces of prime ideals ⋮ Finitely Presented Modules Over Semihereditary Rings ⋮ Polynomial and power series fgc-rings have trivial coefficient rings ⋮ Reduced rings whose finitely generated modules decompose ⋮ The λ-Dimension of Commutative Arithmetic Rings ⋮ Modules with RD-Composition Series over a Commutative Ring ⋮ Two Questions on Scalar-Reflexive Rings ⋮ Local duo rings whose finitely generated modules are direct sums of cyclics ⋮ Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings ⋮ Semilocal Domains Whose Finitely Generated Modules are Direct Sums of Cyclics ⋮ Module-theoretic generalization of commutative von Neumann regular rings ⋮ Commutative rings of bounded module type ⋮ Divisibility theory in commutative rings: Bezout monoids ⋮ Commutative rings whose finitely embedded modules have injective dimension \(\approx\) 1 ⋮ On noncommutative FGC rings ⋮ C-Pure Projective Modules ⋮ On 1-semiregular and 2-semiregular rings

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• Anneaux locaux commutatifs sur lesquels tout module de type fini est somme directe de modules monogènes
• Elementary Divisor Rings and Finitely Presented Modules
• Almost Maximal Integral Domains and Finitely Generated Modules
• Cotorsion modules
• Arithmetical rings
• Decomposable Modules
• Modules over commutative regular rings
• On the Existence of c-Points in βN\N
• Pre-Self-Injective Rings
• Prime Ideal Structure in Commutative Rings
• Sur la compacité du spectre minimal d'un anneau
• Almost Maximal Valuation Rings
• Some Criteria for Hermite Rings and Elementary Divisor Rings
• Elementary Divisors and Modules
• Modules Over Dedekind Rings and Valuation Rings

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