Abstract

Among other results on subtractive semirings, we present complete descriptions of subtractive artinian ideal-simple (congruence-simple) semirings as well as subtractive semisimple semirings. Also, solving Problem 2 of [12] for semisimple semirings, we show that matrix semirings over a semisimple semiring R are subtractive iff R is a ring. Finally, confirming a conjecture of [11] for the classes of additively regular semisimple and additively regular subtractive artinian semirings, we show that perfect semirings in those classes are just perfect rings.