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Abstract <p> Semirings with commutative idempotent multiplication in which the identity <Equation ID="Equi"> <EquationSource Format="TEX">\(x+2xy=x\)</EquationSource> </Equation> holds are studied. Such semirings form a variety of semirings containing all Boolean rings and all distributive lattices. Various characterizations of these semirings are obtained and the lattices of congruences on them are considered. Examples are given and explaining comments are made. </p>

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Commutative Multiplicatively Idempotent Semirings with the Identity \(x+2xy=x\)

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • E. M. Vechtomov

摘要

Abstract

Semirings with commutative idempotent multiplication in which the identity \(x+2xy=x\) holds are studied. Such semirings form a variety of semirings containing all Boolean rings and all distributive lattices. Various characterizations of these semirings are obtained and the lattices of congruences on them are considered. Examples are given and explaining comments are made.