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
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.
