半群T_E(X)中的一个同余(英文)

A congruence on T E(X)

摘要: 设ＴＸ表示集合Ｘ上的全变换半群，Ｃｏｎ（Ｓ）表示半群Ｓ上的同余格．对Ｘ上任一非平凡等价关系Ｅ，令ＴＥ（Ｘ）＝｛ｆ∈Ｔｘ：（ａ，ｂ）∈Ｅ，（ｆ（ａ），ｆ（ｂ））∈Ｅ｝．据［４］，ＴＥ（Ｘ）构成一个α半群，且Ｃｏｎ（ＴＥ（Ｘ））可以分解为三个互不相交的完全子格，其中的一个为［Ｃ（Ｅ），Ｃａ（Ｅ）］．本文报道了ＴＥ（Ｘ）的同余τ，并证明了当Ｅ为单等价关系时，τ是［Ｃ（Ｅ），Ｃａ（Ｅ）］中的唯一原子．

Abstract: T X denotes the full transformation semigroup on a set X and Con(S) denotes the complete lattice of all congruences on a semigroup S. For a nontrivial equivalence E on X, let T E(X)=f∈T X:(a,b) ∈E,(f(a),f(b)∈E. As we have seen in 4,T E(X) forms an α semigroup and Con(T E(X)) can be decomposed into three disjoint complete sublattices, one of which is C(E),C α(E).In this paper we find out a congruence τ on T E(X) which is contained in C(E),C α(E) and we show that whenever E is a simple equiv...