关于左(右)同余自由半群

ON THE LEFT (RICHT) CONGRUENCE-FREE SEMIGROUPS

主要解决了Ochmkc教授提出的一个问题,得到以下结果:定理 设S是半群,则下述三款等价1)S是L_1自由半群;2)S是L_r自由半群;3)|S|<2或|S|>2且S是素数阶循环群.命题 设S是半群,则S有非平凡左(右)同余当且仅当S含真子半群.

A problem put forward by Professor Ochmkc is solved in the paper. Theorem Let S be a semigroup, then the following properties arc equivalent(1) S is a LI free semigroup,(2) SisaL, free semigroup;(3) |S'|,C2 or |5| > 2, and S is a cyclic group of prime order.Proposition Let S be a semigroup, then S has nontrivial left (right) congruences if and only if 5 has proper subscmigroups.