Multiplication modules with prime spectrum

被引：3

作者：

Ones, Ortac ^{[1
]}

Alkan, Mustafa ^{[1
]}

机构：

[1] Akdeniz Univ, Fac Sci, Dept Math, Antalya, Turkey

来源：

TURKISH JOURNAL OF MATHEMATICS | 2019年 / 43卷 / 04期

关键词：

Multiplication module; prime submodule; spectrum of module;

D O I：

10.3906/mat-1803-54

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：2000 / 2009

页数：10

共 13 条

[1]

Ali M.M, 2001, BEITRAGE ALGEBRA GEO, V42, P557

[2] On invertible and dense submodules [J].