Congruence extension property for semirings

Abstract

In this paper, we defined the congruence extension property, biideal extension property for semirings and bi-ideal semirings. Relations among the various extensions are explored. Properties of bi-ideal semirings are studied. Also, we gave some examples that a bi-ideal semiring which has the bi-ideal extension property does not have the congruence extension property, a subsemiring of a bi-ideal semiring may not be a bi-ideal semiring, etc. Finally, a necessary and sufficient condition of a special rectangular ring with congruence extension property was established. Mathematics Subject Classification: 16Y60