关于周期J-平凡半群的构造

On the Structure of Periodic J-trivial Semigroups

本文讨论周期的J-平凡半群。设S是半群,x,y∈S。称x,y为J-等价的,如果S^1xS^1=S^1yS^1(或者说x∈S^1yS^1,y∈S^1xS^1)。x所在的J-等价类记为J_x。称S为J-平凡半群,如果S的任何J-等价类只含一个元素。

In this paper we discuss the periodic J-trivial semigroups. The main result is that a semigroup S is a periodic J-trivial semigroup if and only if S is a semilattice of nilsemigroups, if and only if S is a quasinilpotent semigroup. (A semigroup S is called quasinilpotent semigroup, if: (a) The partial yorder set (E(S), <) is a semilattice, where E(S) is the set of idempotent elements of S, c<f if and only if ef=fe=e (b) For every e∈E(S) there is a nilsemigroup N_c(? S) whose zero is e, (c) s=∪ a?E(S)N_c, (d) For any e, f∈E(S), N_eN_f?N_(eΛf)