Some subvarieties of semirings variety COS

Abstract

Green’s ∗-relations on semirings satisfying additional identities [Formula: see text] and [Formula: see text] are studied. Equivalent characterizations of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are obtained and equivalent conditions are given for the above relations to be congruences. It is proved that semiring classes determined by these congruences are varieties.

Keywords

• Green’s relations
• semiring
• congruence
• identity
• variety