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 an...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.展开更多
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 i...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.展开更多
基金Financially supported by Higher Education Commission of Pakistan
文摘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.
文摘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.
