島根大学理学部紀要

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島根大学理学部紀要 20
1986-12-25 発行

クリフォード半群のマトリックスおよびリースの定理の一般化について

Matrices of Clifford Semigroups, and a Generalization of Rees's Theorem
山田 深雪
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内容記述(抄録等)
Let S be a completely regular semigroup, and E(S) the partial subgroupoid of idempotents of S. Let γ be a relation on E(S). If γ is a congruence on E(S), that is, if γ is an equivalence relation on E(S) and if χγy and μγν satisfy χμγyν (if both χμ and yν are defined in E(S)), then S is called a CS-matrix. Firstly, several characterizations of a CS-matrix are given. Secondly, split CS-matrices are investigated. In particular, matrix representations of these semrgroups are discussed.