Ordered regular equivalence relations on ordered semihypergroups

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• 作者：Ze Gu ; ^{guze528@sina.com" class="auth_mail" title="E-mail the corresponding author} ; Xilin Tang ^{xilintang@21cn.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：20N20 ; 06F05
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：450
• 期：Complete
• 页码：384-397
• 全文大小：347 K

文摘

In this paper, we introduce the concept of ordered regular (strongly ordered regular) equivalence relation on an ordered semihypergroup. Moreover, we use hyperfilters to construct a strongly ordered regular equivalence relation on an ordered semihypergroup, for which the corresponding quotient structure is a semilattice. Finally, we construct an ordered regular equivalence relation on an ordered semihypergroup by hyperideals such that the corresponding quotient structure is also an ordered semihypergroup under a related order relation, which is an answer to the open problem given by B. Davvaz, P. Corsini and T. Changphas in European Journal of Combinatorics.