E-反演半群胚的群胚同余

Groupoid Congruences on E-inversive Semigroupoids

建立E-反演半群胚C的正规子半群胚格和C的群胚同余格之间的格同构,并将此应用到E-反演半群S上,得到S的正规子半群格和群同余格的刻画.给出E-反演半群胚C的最小自共轭全子半群胚U(C)的构造及其与最小正规子半群胚D(C)的关系,证明了U(C)的酉性与C的最小群胚同余σ的纯性等价.

In this paper,the lattice isomorphism between the lattice of normal subsemigroupoids of an E-inversive semigroupoid C and the lattice of groupoid congruences of C. The result is applied to an E-inversive semigroup S,a characterization of the lattice of normal subsemigroups and that of group congruences of S. Moreover,the structure of the least self-conjugate and full subsemigroupoid （C） of an E-inversive semigroupoid C is given,the relation of it and the least normal subsemigroupoid D（C） is discussed. It is proved that the unitarity of （C） is equivalent to the purity of the least groupoid congruence σ of C.