Multiplication modules with prime spectrum | Zendy

Ortaç Öneş | Zendy; Mustafa Alkan | Zendy

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Multiplication modules with prime spectrum

Author(s) -

Ortaç Öneş,

Mustafa Alkan

Publication year - 2019

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1803-54

Subject(s) - mathematics , multiplication (music) , prime (order theory) , commutative ring , spectrum (functional analysis) , associated prime , ring (chemistry) , characterization (materials science) , discrete mathematics , pure mathematics , commutative property , combinatorics , physics , quantum mechanics , chemistry , organic chemistry , optics

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 radM (0) and also show that there are proper ideals I1, ..., In of R such that radM (0) = radM ((I1...In)M) . Finally, we prove that the spectrum Spec(M) is irreducible if and only if M is the finite sum of its submodules, whose T -radicals are prime in M .

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