An Analogy of Clifford Decomposition Theorem for Abel-Grassmann Groupoids  

作　　者：Madad Khan Saima Anis 

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

出　　处：《Algebra Colloquium》2014年第2期347-353,共7页代数集刊（英文版）

摘　　要：Let S be an inverse AG-groupoid （Abel-Grassmann groupoid） and define a relation γ on S by aγb if and only if there exist some positive integers n and m such that bm∈ （Sa）S and an∈ （Sb）S. We prove that S/γ is a maximal semilattice homomorphic image of S. Thus, every inverse AG-groupoid S is uniquely expressible as a semilattice Y of some Archimedean inverse AG-groupoids Sα （α∈ Y）. Our result can be regarded as an analogy of the well known Clifford theorem in semigroups for AG-groupoids.Let S be an inverse AG-groupoid （Abel-Grassmann groupoid） and define a relation γ on S by aγb if and only if there exist some positive integers n and m such that bm∈ （Sa）S and an∈ （Sb）S. We prove that S/γ is a maximal semilattice homomorphic image of S. Thus, every inverse AG-groupoid S is uniquely expressible as a semilattice Y of some Archimedean inverse AG-groupoids Sα （α∈ Y）. Our result can be regarded as an analogy of the well known Clifford theorem in semigroups for AG-groupoids.

关 键 词：inverse AG＊＊-groupoid invertive law medial law 

分 类 号：O159[理学—数学] O11[理学—基础数学]