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Generalizations of ⊕ -supplemented modules

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Ukrainian Mathematical Journal Aims and scope

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 an srs ⊕-module; (3) over a local Dedekind domain, every ⊕ -radical supplemented module is an srs ⊕-module. Moreover, we completely determine the structure of these modules over local Dedekind domains.

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Authors and Affiliations

  1. Ondokuz Mayıs University, Samsun, Turkey

    B. N. Türkmen & A. Pancar

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  1. B. N. Türkmen
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  2. A. Pancar
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 4, pp. 555–564, April, 2013.

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Türkmen, B.N., Pancar, A. Generalizations of ⊕ -supplemented modules. Ukr Math J 65, 612–622 (2013). https://doi.org/10.1007/s11253-013-0799-1

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  • DOI: https://doi.org/10.1007/s11253-013-0799-1

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