ON PRIME SUBMODULES AND PRIMARY DECOMPOSITIONS IN TWO-GENERATED FREE MODULES

In this paper, we consider the freeR-moduleR⊕R, whereRis an arbitrary commutative ring with identity. We give a full characterization for prime submodules ofR⊕Rand a useful primeness test for a finitely generated submodule ofR⊕R. We study the existence of primary decomposition of a submodule ofR⊕Ran...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 17; no. 1; pp. 133 - 142
Main Authors Çeken, Seçil, Alkan, Mustafa
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.02.2013
Subjects
Mathematical rings
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ISSN1027-5487
2224-6851
DOI10.11650/tjm.17.2013.1803

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Summary:In this paper, we consider the freeR-moduleR⊕R, whereRis an arbitrary commutative ring with identity. We give a full characterization for prime submodules ofR⊕Rand a useful primeness test for a finitely generated submodule ofR⊕R. We study the existence of primary decomposition of a submodule ofR⊕Rand characterize the minimal primary decomposition. As applications of our results, we give some examples of primary decompositions inR⊕R. 2010Mathematics Subject Classification: 13A99, 13C10, 13C99. Key words and phrases: Prime submodule, Primary submodule, Primary decomposition.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.1803