含纯正断面的半群

On Semigroups with Orthodox Transversals

本文我们研究半群的一种断面纯正断面 ,它是比逆断面更广泛的一种断面 .我们引入 0 -格林关系这个工具 ,采用 Lawson提出的研究正则半群的新的研究办法正则半群是子半群的一个特殊扩张整体逆扩张 (enlargement) .研究含纯正断面的半群的等价刻划 ,得到含纯正断面半群的一些性质 .最后还证明了 ,如果 S0是 E0 -完全半群 。

In this taper, we study a transversal of semigroups-orthodox transversal, it is more universal than inverse transversal. We introduce the new equivalence, 0 Green′s relation on semigroups. By using a menthod to study regular semigroups by lawson, this is an enlargement of subsemigroup, we obtain the characterizations and some properties of a semigroup with orthodox transversals. Finally, we show that if S 0 is E 0 full semigroup, then S 0 is an orthodox transversal if and only if S 0 is an inverse transversal.