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

Ceken S., ALKAN M.

TAIWANESE JOURNAL OF MATHEMATICS, vol.17, no.1, pp.133-142, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.11650/tjm.17.2013.1803
  • Journal Name: TAIWANESE JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.133-142
  • Keywords: Prime submodule, Primary submodule, Primary decomposition
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, we consider the free R-module R circle plus R, where R is an arbitrary commutative ring with identity. We give a full characterization for prime submodules of R circle plus R and a useful primeness test for a finitely generated submodule of R circle plus R. We study the existence of primary decomposition of a submodule of R circle plus R and characterize the minimal primary decomposition. As applications of our results, we give some examples of primary decompositions in R circle plus R.