D-Subvarieties of the Variety of Idempotent Semirings

• 来源期刊: 代数集刊（英文版）
• 关键词: idempotent semirings Green's relations congruences variety identity
• 年，卷（期）: 2002,（1）
• 页码范围: 15-28
• 页数: 14页
• 语种: 英文

摘要

We show that certain varieties of idempotent semirings can be determined by some properties of Green's D-relations. We provide equational bases for the D-subvarieties of the variety of idempotent semirings and investigate their Mal'cev product decompositions. In particular, the relationship among these varieties is discussed and we prove that Green's relation D on an idempotent semiring S is a congruence on S if and only if both D+∩D· and D+ ∨D·are congruences on S.Some results recently obtained by Pastijn and Zhao are consequently extended.