非周期幺半群的交叉簇
Cross varieties of aperiodic monoids
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中文总结 AI 辅助
本文研究非周期幺半群的交叉簇，证明其为交叉簇等价于排除22个近交叉簇，且该列表穷尽了所有此类近交叉簇。
中文摘要 AI 辅助
通用代数的一个簇若满足有限基、有限生成且仅含有限多个子簇，则称为交叉簇；若幺半群的所有子群均为平凡的，则称为非周期幺半群。本文证明，一个非周期幺半群的簇是交叉簇当且仅当它作为子簇排除了特定的22个近交叉簇；由此得出，这22个簇穷尽了非周期幺半群的所有近交叉簇。
英文摘要
A variety of universal algebras is called Cross if it is finitely based, finitely generated, and has only finitely many subvarieties. A monoid is aperiodic if all its subgroups are trivial. In the present article, we show that a variety of aperiodic monoids is Cross if and only if it excludes, as subvarieties, a certain list of 22 almost Cross varieties. Consequently, this list of 22 varieties exhausts all almost Cross varieties of aperiodic monoids.
