Semirings generated by idempotents

被引：0
作者：
Dolzan, David [1 ,2 ]
机构：
[1] Radiotelevis Slovenia, Ljubljana SI-1000, Slovenia
[2] Inst Math Phys & Mech, Ljubljana SI-1000, Slovenia
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2024年
关键词：
Semiring; idempotent; nilpotent; RINGS;
D O I：
10.1142/S0219498825502846
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that a semiring multiplicatively generated by its idempotents is commutative and Boolean, if every idempotent in the semiring has an orthogonal complement. We prove that a semiring additively generated by its idempotents is commutative, if every idempotent in the semiring has an orthogonal complement and all the nilpotents in the semirings are central. We also provide examples that the assumptions on the existence of orthogonal complements of idempotents and the centrality of nilpotents cannot be omitted.
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页数：8
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