MULTIPLICATIVELY IDEMPOTENT SEMIRINGS

被引：1
|
作者：
Chajda, Ivan [1 ]
Laenger, Helmut [2 ]
Svrcek, Filip [1 ]
机构：
[1] Palacky Univ, Dept Algebra & Geometry, Fac Sci, 17 Listopadu 12, Olomouc 77146, Czech Republic
[2] Vienna Univ Technol, Fac Math & Geoinformat, Inst Discrete Math & Geometry, A-1040 Vienna, Austria
来源：
MATHEMATICA BOHEMICA | 2015年 / 140卷 / 01期
基金：
奥地利科学基金会;
关键词：
semiring; commutative semiring; multiplicatively idempotent semiring; semiring of characteristic 2; simple semiring; unitary Boolean ring; bounded distributive lattice;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Semirings are modifications of unitary rings where the additive reduct does not form a group in general, but only a monoid. We characterize multiplicatively idempotent semirings and Boolean rings as semirings satisfying particular identities. Further, we work with varieties of enriched semirings. We show that the variety of enriched multiplicatively idempotent semirings differs from the join of the variety of enriched unitary Boolean rings and the variety of enriched bounded distributive lattices. We get a characterization of this join.
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页码：35 / 42
页数：8
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