关于一类半环上的格林关系的若干研究

Several studies of Green′s relations on a class of semiring

研究了加法半群是带,乘法半群是完全正则半群的半环上的格林关系,给出了˙L∧+D(+L,+R)是同余关系的充分必要条件,证明了由这些同余关系所决定的半环类都是半环簇,并给出了这些半环簇的Mal′cev积分解.

Greents-relations of a semiring variety whose additive reduct is band and multiplicative reduct is completely regular semigroup are studied.We give the sufficient and necessary conditions which make L A ∧ D^＋ （L^＋, R^＋） be congruence relations, obtain the classes of semiring which are determined by these Green＇s-relations are semiring varieties, and through the Mal＇cev product, we also obtain the decomposition of these semiring varieties.