On non-associative generalizations of MV-algebras and lattice-ordered commutative loops

详细信息    查看全文

• 作者：Jan Krňá ; vek ^{jan.krnavek@upol.cz" class="auth_mail" title="E-mail the corresponding author} ; Jan Kü ; hr ; ^{jan.kuhr@upol.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：MV-algebra ; Semilinear commutative basic algebra ; Lattice-ordered commutative loop ; Good function
• 刊名：Fuzzy Sets and Systems
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：289
• 期：Complete
• 页码：122-136
• 全文大小：366 K

文摘

The aim of the paper is to describe the connections between lattice-ordered commutative loops and certain “basic algebras” which are a non-associative generalization of MV-algebras and are related to commutative semicopulas. This extends the well-known equivalence between lattice-ordered Abelian groups with strong order-unit and MV-algebras.