On 2-absorbing ideals of commutative semirings

被引：3

作者：

Behzadipour, H. ^{[1
]}

Nasehpour, P. ^{[2
]}

机构：

[1] Univ Tehran, Univ Coll Engn, Sch Elect & Comp Engn, Tehran, Iran

[2] Golpayegan Univ Technol, Dept Engn Sci, Golpayegan, Iran

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 02期

关键词：

Semiring; 2-absorbing ideals; 2-AB semirings; RINGS;

D O I：

10.1142/S0219498820500346

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate 2-absorbing ideals of commutative semirings and prove that if a is a nonzero proper ideal of a subtractive valuation semiring S then a is a 2-absorbing ideal of S if and only if a = p or a = p(2) where p = root a is a prime ideal of S. We also show that each 2-absorbing ideal of a subtractive semiring S is prime if and only if the prime ideals of S are comparable and if p is a minimal prime over a 2-absorbing ideal a, then am= p, where m is the unique maximal ideal of S.

引用

页数：12

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