D-Subvarieties of the Variety of Idempotent Semirings

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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.
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