RINGS OVER WHICH CYCLICS ARE DIRECT SUMS OF PROJECTIVE AND CS OR NOETHERIAN

DOI10.1017/S0017089510000200zbMath1208.16006arXiv1001.4132MaRDI QIDQ3577723

Christopher J. Holston, André Leroy, Surender Kumar Jain

Publication date: 23 July 2010

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.4132

zbMATH Keywords

direct sumsprojective modulesinjective modulesNoetherian modules\(V\)-ringsCS modules

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) 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) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (5)

Rings with modules having a restricted injectivity domain ⋮ Some results on V-rings and weakly V-rings. ⋮ More characterizations of Dedekind domains and V-rings ⋮ Unnamed Item ⋮ Some results and questions on left-right symmetry

Cites Work

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• Cyclic modules whose quotients have all complement submodules direct summands
• On modules with finite uniform and Krull dimension
• Dual generalizations of the Artinian and Noetherian conditions
• Commutative rings whose homomorphic images are self-injective
• On rings whose simple modules are injective
• AN AFFIRMATIVE ANSWER TO A QUESTION ON NOETHERIAN RINGS
• Rings Whose Cyclic Modules are Injective or Projective
• Rings Characterized by their Cyclic Modules
• Conditions for a ring to be Noetherian or Artinian
• Topological Representation of Algebras. II
• Rings whose finitely generated modules are extending

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