Prime Ideals in Semirings

被引：0
|
作者：
Gupta, Vishnu [1 ]
Chaudhari, J. N. [2 ]
机构：
[1] Univ Delhi, Dept Math, Delhi 110007, India
[2] MJ Coll, Dept Math, Jalgaon 425002, India
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2011年 / 34卷 / 02期
关键词：
Semiring; reduced semiring; Bourne factor semiring; subtractive ideal; prime ideal; completely prime ideal; minimal prime ideal;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we prove the following theorems: (1) A nonzero ideal I of (Z(+), +, .) is prime if and only if I = < p > for some prime number p or I = < 2, 3 >. (2) Let R be a reduced semiring. Then a prime ideal P of R is minimal if and only if P = A(P) where A(P) = {r is an element of R : there exists a is not an element of P such that ra = 0}.
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页码：417 / 421
页数：5
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