Ideal Theory in Quotient Semirings

J. N. Chaudhari, D. R. Bonde

Abstract

Atani [1] proved some results in quotient semirings using subtractive ideals. We introduce the notion of subtractive extension of an ideal which is a generalization of subtractive ideals. In the results of Atani, we replace the condition of subtractive ideal by subtractive extension of an ideal and hence generalize all the results of Atani. We obtain some equivalent conditions for subtractive extension of an ideal and hence characterize the ideals, prime ideals and primary ideals in quotient semirings.