Generalizations of ⊕ -supplemented modules
We introduce ⊕-radical supplemented modules and strongly ⊕-radical supplemented modules (briefly, srs⊕-modules) as proper generalizations of ⊕-supplemented modules. We prove that (1) a semilocal ring R is left perfect if and only if every left R-module is an ⊕-radical supplemented module; (2) a co...
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| Date: | 2013 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2013
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| Series: | Український математичний журнал |
| Subjects: | |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Generalizations of ⊕ -supplemented modules / B.N. Türkmen, A. Pancar // Український математичний журнал. — 2013. — Т. 65, № 4. — С. 555-564. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We introduce ⊕-radical supplemented modules and strongly ⊕-radical supplemented modules (briefly, srs⊕-modules) as
proper generalizations of ⊕-supplemented modules. We prove that (1) a semilocal ring R is left perfect if and only if every
left R-module is an ⊕-radical supplemented module; (2) a commutative ring R is an Artinian principal ideal ring if and
only if every left R-module is a srs⊕-module; (3) over a local Dedekind domain, every ⊕-radical supplemented module
is a srs⊕-module. Moreover, we completely determine the structure of these modules over local Dedekind domains. |
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