| Several Classes of Additively Non-Regular Semirings |
| Received:September 07, 2008 Revised:June 30, 2009 |
| Key Words:
Green's $\ast$-relations subdirect product adequate semiring skew-halfring.
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| Fund Project:Supported by the Natural Science Foundation of Hunan Province (Grant No.04JJ4001) and the Scientific Research Foundation of Hunan Education Department (Grant No.05A014). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.05.002 |
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