几类加法非正则半环

Several Classes of Additively Non-Regular Semirings

中文关键词:  格林*-关系  次直积  恰当半环  skew-halfring半环.

英文关键词:Green's $\ast$-relations  subdirect product  adequate semiring  skew-halfring.

中文摘要:

      为了研究加法非正则半环,引入了格林*-关系和[左,右]恰当半环.我们刻画了具有[左、右]skew-halfring半环的强b-格的半环以及是交换幂等半环和[左、右]skew-halfring半环的次直积的半环.所获得的结果包括了[14]中的广义Clifford半环结构和[5]中的具有分配格与环的次直积的半环结构的结果.

英文摘要:

      In this paper, we introduce Green's $\ast$-relations on semirings and define [left, right] adequate semirings to explore additively non-regular semirings. We characterize the semirings which are strong b-lattices of [left, right] skew-halfrings. Also, as further generalization, the semirings are described which are subdirect products of an additively commutative idempotent semiring and a [left, right] skew-halfring. We extend results of constructions of generalized Clifford semirings (given by M. K. Sen, S. K. Maity, K. P. Shum, 2005) and the semirings which are subdirect products of a distributive lattice and a ring (given by S. Ghosh, 1999) to additively non-regular semirings.