Multiplication modules with prime spectrum

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ÖNEŞ O., ALKAN M.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.4, pp.2000-2009, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1803-54
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2000-2009
  • Keywords: Multiplication module, prime submodule, spectrum of module
  • Akdeniz University Affiliated: Yes

Abstract

The subject of this paper is the Zariski topology on a multiplication module M over a commutative ring R. We find a characterization for the radical submodule rad(M)(0) and also show that there are proper ideals I-1, ..., I-n of R such that rad(M)(0) = rad(M)((I-1...I-n) M) . Finally, we prove that the spectrum Spec(M) is irreducible if and only if M is the finite sum of its submodules, whose tau-radicals are prime in M.