对合K-正则半环

K-regular semiring with involution

研究对合K-正则半环的性质,利用K-正则半环的Green-关系从多个角度刻画对合K-正则半环,对合半群的幂半环是对合K-正则半环当且仅当对合半群是对合正则半群,最后给出对合正则半群的幂半环是对合交换半环的几个等价命题。

Some properties on K-regular semiring with involution are studied.The K-regular semiring with involution are discussed in different ways by using Green-relation on K-regular semiring.The power semiring of semigroup with involution which is a K-regular semiring with involution if and only if semigroup is a regular semigroup.Finally,it is obtained that the equivalent proposition of the power semiring of involutorial regular semigroup which is a commutative semiring with involution.