Representation of BL-algebras with finite independent spectrum

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• 作者：Stefano Aguzzoli^a ; ^{aguzzoli@di.unimi.it} ; Manuela Busaniche^b ; ^{mbusaniche@santafe-conicet.gov.ar} ; José ; Luis Castiglioni^c ; ^{jlc@mate.unlp.edu.ar} ; Noemí ; Lubomirsky^c ; ^{nlubomirsky@mate.unlp.edu.ar}
• 关键词：BL-algebras ; Residuated lattices ; Poset product ; Wajsberg hoops
• 刊名：Fuzzy Sets and Systems
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：15-32
• 全文大小：395 K
• 卷排序：311

文摘

A representation theorem for a class of BL-algebras with finite spectrum is presented. Although the class comprised by our result is not the whole class of BL-algebras with finite spectrum, it applies to some important classes such as finite BL-algebras and BL-chains with finite spectrum among others. Our representation constitutes a generalization of the ordinal sum construction, since we decompose each algebra in terms of totally ordered Wajsberg hoops.