Characterizations of hemirings by theirh-ideals

Abstract

a b s t r a c tIn this paper we characterize hemirings in which all h-ideals or all fuzzy h-ideals are idempotent. It is proved, among other results, that every h-ideal of a hemiring R is idempotent if and only if the lattice of fuzzy h-ideals of R is distributive under the sum and h-intrinsic product of fuzzy h-ideals or, equivalently, if and only if each fuzzy h-ideal of R is intersection of those prime fuzzy h-ideals of R which contain it. We also define two types of prime fuzzy h-ideals of R and prove that, a non-constant h-ideal of R is prime in the second sense if and only if each of its proper level set is a prime h-ideal of R.

Characterizations of Hemirings by the Properties of Their <i>k</i>-Ideals

“…Fuzzy k-ideals are studied in [17][18][19][20][21][22]. Fuzzy h-ideals are studied in [23][24][25][26][27][28][29]. In this paper we characterize those hemirnigs for which each k-ideal is idempotent and also those hemirings for which each fuzzy k-ideal is idempotent.…”