| 几类加法非正则半环 |
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| 引用本文： | 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. |
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| 作者姓名： | 李勇华 黄凤梅 何勇 |
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| 作者单位： | 华南师范大学数学科学学院, 广州, 510631;华南师范大学数学科学学院, 广东 广州 510631;湖南科技大学计算机学院, 湖南 湘潭 411201 |
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| 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). |
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| 摘 要： | In this paper, we introduce Green＇s .-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. MaRy, 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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| 关 键 词： | Green＇s -relations subdirect product adequate semiring skew-halfring. |
| 收稿时间： | 9/7/2008 12:00:00 AM |
| 修稿时间： | 2009/6/30 0:00:00 |
Several Classes of Additively Non-Regular Semirings |
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| Yong Hua LI,Feng Mei HUANG and Yong HE.Several Classes of Additively Non-Regular Semirings[J].Journal of Mathematical Research with Applications,2010,30(5):775-790. |
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| Authors: | Yong Hua LI Feng Mei HUANG and Yong HE |
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| Institution: | 1. School of Mathematical Sciences,South China Normal University,Guangdong 510631,P.R.China
2. School of Computer,Hunan University of Science and Technology,Hunan 411201,P.R.China |
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| Abstract: | 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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| Keywords: | Green's $\ast$-relations subdirect product adequate semiring skew-halfring |
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