李勇华,黄凤梅,何勇.几类加法非正则半环[J].数学研究及应用,2010,30(5):775~790
几类加法非正则半环
Several Classes of Additively Non-Regular Semirings
投稿时间:2008-09-07  最后修改时间:2009-06-30
DOI:10.3770/j.issn:1000-341X.2010.05.002
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.
基金项目:湖南省自然科学基金项目(Grant No.04JJ40001), 湖南省教育厅科学研究基金项目(Grant No.05A014).
作者单位
李勇华 华南师范大学数学科学学院, 广州, 510631 
黄凤梅 华南师范大学数学科学学院, 广东 广州 510631 
何勇 湖南科技大学计算机学院, 湖南 湘潭 411201 
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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.
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