Characterizations of hemirings by their h-ideals

Authors:
Wieslaw A. Dudek;Muhammad Shabir;Rukhshanda Anjum
Affiliations:
Institute of Mathematics and Computer Science, Wroclaw University of Technology, 50-370 Wroclaw, Poland;Department of Mathematics, Quaid-i-Azam University Islamabad, Pakistan;Department of Mathematics, Quaid-i-Azam University Islamabad, Pakistan
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

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.