Multiplicatively Idempotent Semirings in which All Congruences Are Ideal

被引：1
|
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 / 112卷 / 3-4期
关键词：
semiring; multiplicatively idempotent semiring; ideal congruence; Boolean ring; generalized Boolean lattice;
D O I：
10.1134/S0001434622090061
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The study of multiplicatively idempotent semirings with additional conditions is continued. It is proved that every multiplicatively idempotent semiring with ideal congruences is isomorphic to the direct product of a Boolean ring and a generalized Boolean lattice. Thus, a new abstract characterization is obtained for the direct products of Boolean rings and generalized Boolean lattices. Examples are given.
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收藏
页码：382 / 387
页数：6
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