Characterizations of hemirings by their h-ideals

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• 作者：Wieslaw A. Dudek ; Muhammad Shabir ; Rukhsh ; a Anjum
• 关键词：Prime ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TYJ-4YRGJDF-3&_mathId=mml20&_user=10&_cdi=5620&_pii=S089812211000163X&_rdoc=17&_issn=08981221&_acct=C000050221&_version=1&_userid=10&
• 刊名：Computers and Mathematics with Applications
• 出版年：2010
• 出版时间：May 2010
• 年：2010
• 卷：59
• 期：9
• 页码：3167-3179
• 全文大小：395 K

文摘

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.