GENERALIZED SUPPLEMENTED MODULES

Let R be a ring and M a right R-module. It is shown that: (1) M is Artinian if and only if M is a GAS-module and satisfies DCC on generalized supplement submodules and on small submodules; (2) if M satisfies ACC on small submodules, then M is a lifting module if and only if M is a GAS-module and eve...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 10; no. 6; pp. 1589 - 1601
Main Authors Wang, Yongduo, 王永鋒, Ding, Nanqing, 丁南慶
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China (Taiwan) 01.12.2006
Subjects
Algebra
Mathematical rings
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Summary:Let R be a ring and M a right R-module. It is shown that: (1) M is Artinian if and only if M is a GAS-module and satisfies DCC on generalized supplement submodules and on small submodules; (2) if M satisfies ACC on small submodules, then M is a lifting module if and only if M is a GAS-module and every generalized supplement submodule is a direct summand of M if and only if M satisfies (P*); (3) R is semilocal if and only if every cyclic module is a GWS-module.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500404577