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Several Classes of Additively Non-Regular Semirings: 《Journal of Mathematical Research and Exposition》2010年第5期775-790,共16页Yong Hua LI Feng Mei HUANG Yong HE; Supported by the Natural Science Foundation of Hunan Province (Grant No04JJ4001);the Scientific Research Foundation of Hunan Education Department (Grant No05A014); 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...; 关键词：Green＇s -relations subdirect product adequate semiring skew-halfring.