On Fuzzy semihyperrings
General Mathematics
2013-04-24 v1
Abstract
In this article we introduce the study of fuzzy semihyperrings and fuzzy R-semihypermodules, where R is a semihyperrings and R-semihypermodules are represntations of R. In particular, semihyperrings all of whose hyperideals are idempotent, called fully idempotent semihyperrings, are investigated in a fuzzy context. It is proved, among other results, that a semihyperring R is fully idempotent if and only if the lattics of fuzzy hyperideals of R is distributive under the sum and product of fuzzy hyperideals. It is also shown that the set of proper fuzzy prime hyperideals of a fully idempotent semihyperring R admits the structure of a topological space, called the fuzzy prime spectrum of R.
Cite
@article{arxiv.1304.6371,
title = {On Fuzzy semihyperrings},
author = {Aqeel Ahmed and Muhammad Aslam},
journal= {arXiv preprint arXiv:1304.6371},
year = {2013}
}