Completely Prime Ideals in Multiplicatively Idempotent Semirings

被引：2
|
作者：
Vechtomov, E. M. [1 ]
Petrov, A. A. [1 ]
机构：
[1] Vyatka State Univ, Kirov 610000, Russia
来源：
MATHEMATICAL NOTES | 2022年 / 111卷 / 3-4期
关键词：
semiring; multiplicatively idempotent semiring; completely prime ideal; maximal ideal; commutativity; Boolean ring; generalized Boolean lattice;
D O I：
10.1134/S0001434622030191
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Structure properties of multiplicatively idempotent semirings are considered. Basic results concerning completely prime ideals in multiplicatively idempotent semirings are obtained. The main theorem describes the commutative multiplicatively idempotent semirings with zero in which all completely prime ideals are maximal: up to isomorphism, such semirings are exhausted by direct products of a Boolean ring and a generalized Boolean lattice. Examples are given showing that the conditions of commutativity and the presence of zero are essential.
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收藏
页码：515 / 524
页数：10
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