幺半群等价

Equivalent Monoids

讨论了幺半群等价.给出了幺半群等价的一些性质,证明了两个重要的格同构.得到:如果幺半群R和S等价,F是从左R-系范畴到左S-系范畴的范畴等价,M是一个左R-系,ρ是R的一个同余,则有M的子系格L(M)和F(M)的子系格L(F(M))格同构,R的同余格C(R)和S的同余格C(S)格同构,幺半群R/ρ和S/ψ(ρ)等价,其中ψ是R的同余格C(R)和S的同余格C(S)的格同构.

In this paper, the author studies equivalent monoids. Some characterizations of equivalent monoids are given. Two important lattice isomorphisms are shown. Let R and S be equivalent monoids via an equivalence F.R-Act → S-Act . For each left R- act M and each congruence ρ on R , set φb（ρ） = ls（F（R/ρ））,C（R）={λ/λ is a congruence on R },and L（M） = {N ] N is a subact of M }. It is shown that L（M） is isomorphic to L（F（M）） and C（R） is isomorphic to C（S） as lattices. Moreover the semigroups R/ρ and S/φb（ρ） are equivalent.