On Semilattice Decomposition of an Abel–Grassmann’s Groupoid  

作　　者：Madad KHAN Saima ANIS 

机构地区：[1]Department of Mathematics,COMSATS Institute of Information Technology

出　　处：《Acta Mathematica Sinica,English Series》2012年第7期1461-1468,共8页数学学报（英文版）

基　　金：Financially supported by Higher Education Commission of Pakistan

摘　　要：In this paper, we have decomposed an AG-groupoid. Let S be an AG-groupoid with left identity and a relation γ be defined on S as： aγb if and only if there exist positive integers m and n such that b^m∈E （Sa）S and a^n ∈ （Sb）S for all a and b in S. We have proved that S/γ is a maximal separative Semilattice homomorphic image of S. Every AG-groupoid S is uniquely expressible as a semilattice Y of archimedean AG-groupoids Sa （a∈ Y）. The semilattice Y is isomorphic to S/γ and the Sγ （a ∈ Y） are the equivalence classes of S mod V.In this paper, we have decomposed an AG-groupoid. Let S be an AG-groupoid with left identity and a relation γ be defined on S as： aγb if and only if there exist positive integers m and n such that b^m∈E （Sa）S and a^n ∈ （Sb）S for all a and b in S. We have proved that S/γ is a maximal separative Semilattice homomorphic image of S. Every AG-groupoid S is uniquely expressible as a semilattice Y of archimedean AG-groupoids Sa （a∈ Y）. The semilattice Y is isomorphic to S/γ and the Sγ （a ∈ Y） are the equivalence classes of S mod V.

关 键 词：AG-groupoid invertive law medial law CONGRUENCE 

分 类 号：O152[理学—数学]