Characterizations of hemirings by their $h$-ideals

Details Characterizations of hemirings by their $h$-ideals Characterizations of hemirings by their $h$-ideals

2010-03-23

arxiv.org/abs/1003.4534v1

Computers Math. Applications 59 (2010), 3167-3179

Mathematics

Rings and Algebras

Scientific paper

10.1016/j.camwa.2010.03.003

In 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 $R$.

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