Relationships between a Semiring R and Quotient Semiring RQ(I).

The main aim of this paper is to investigate relationships between the ideals of semirings R and RQ(I), where RQ(I) is the quotient semiring and I is the partitioning ideal of R. It is shown that if R is additively cancellative and yoked, then RQ(I) is additively cancellative and yoked. If R is additively cancellative, then RQ(I) is isomorphic to R/pI (R/pI is the factor semiring factored by Bourne relation induced by partitioning ideal I) and (RQ(I))Δ (the ring of dfferences of (RQ(I))Δ), is isomorphic to RΔ/IΔ. [ABSTRACT FROM AUTHOR]