【摘要】 设S是一个半群,a∈S.如果存在x∈S,使得x=xax,则称x为a的一个弱逆.用W(a)表示a的所有弱逆的集合.本文利用元素的弱逆给出了毕竟正则半群S的群同余的若干等价刻画及一个表示.通过S的w-自共轭的、闭的,全子半群H定义了S上的一个二元关系(a,b)∈ρH(?)((?)a’∈W(a),a’b∈H),证明了如果H是S的w-自共轭的、闭的全子半群,则ρH是S上的以H为核的群同余.反过来,如果ρ是S上的群同余,则kerρ是S的w-自共轭的,闭的全子半群,并且ρ=ρkerρ.更多还原

【Abstract】 Let S be an eventually regular semigroup and a∈S. A weak inverse of S is an element x ∈ S such that x = xax, denoted by W(a) the set of weak inverses of a. A representation and some characterizations of group congruences on the eventually regular semigroup are given by means of weak inverse. Define a relation on S: (a, b) ∈ρH (?) ((?)a’ ∈ W(a), a’b ∈ H). It is shown that if H is a w-self-conjugate, closed and full subsemigroup of S, then ρH is a group congruence on S and ker ρH = H. Conversely, if ρ is a group congruence on S, then ker ρ is a w-self-conjugate, closed and full subsemigroup of S and ρ=ρkerρ.更多还原