论文标题
正常的下monoi类和一致性
Normal submonoids and congruences on a monoid
论文作者
论文摘要
引入了一个基团$ m $的{\ em normal submonoid}的概念，该概念概括了组的正常亚组。当通过包含订购时，$ m $的普通亚monioids的集合$ \ mathsf {norsub}（m）$是一个完整的晶格。明确描述了连接，并计算有限完整变换的晶格，$ t_n $，$ n \ geq 1 $。还表明，对于特定的交换性单体（包括所有Krull Monoids），$ \ MATHSF {NORSUB}（M）$是模块化的，并且作为加入半层次，将同态嵌入Isomorphine iSomorphisss iSomorphists iSomorphists of Join subsemilattice of lattice $ \ mathsf {cong}（m）$ M $ m $ m $ m $ m $ m。这导致了计算$ \ mathsf {cong}（m）$的新策略，该$由计算$ \ mathsf {norsub}（m）$组成，以及所谓的Unital Electes of $ m $ modulo的晶格。这为Malcev计算的$ T_N $计算提供了一个新的观点。
A notion of {\em normal submonoid} of a monoid $M$ is introduced that generalizes the normal subgroups of a group. When ordered by inclusion, the set $\mathsf{NorSub}(M)$ of normal submonoids of $M$ is a complete lattice. Joins are explicitly described, and the lattice is computed for the finite full transformation monoids $T_n$, $n\geq 1$. It is also shown that $\mathsf{NorSub}(M)$ is modular for a specific family of commutative monoids, including all Krull monoids, and that, as a join semilattice, embeds isomorphically onto a join subsemilattice of the lattice $\mathsf{Cong}(M)$ of congruences on $M$. This leads to a new strategy for computing $\mathsf{Cong}(M)$ consisting of computing $\mathsf{NorSub}(M)$, and the lattices of the so called unital congruences on the quotients of $M$ modulo its normal submonoids. This provides a new perspective on Malcev computation of the congruences on $T_n$.
