Monadic MV-algebras II: Monadic implicational subreducts

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• 作者：Cecilia R. Cimadamore (1)
  J. Patricio Díaz Varela (1)
  
• 关键词：Primary ; 06D35 ; Secondary ; 08B15 ; 06D99 ; monadic MV ; algebras ; monadic implicational subreducts ; ?ukasiewicz implication algebras ; subvarieties ; equational bases
• 刊名：Algebra Universalis
• 出版年：2014
• 出版时间：May 2014
• 年：2014
• 卷：71
• 期：3
• 页码：201-219
• 全文大小：292 KB
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• 作者单位：Cecilia R. Cimadamore (1)
  J. Patricio Díaz Varela (1)
  
  1. Departamento de Matemática, Universidad Nacional del Sur, Instituto de Matemática de Bahía Blanca (INMABB) (CONICET-UNS), Alem 1253, Bahía Blanca, 8000, Argentina
  
• ISSN：1420-8911

文摘

In this paper, we study the class of all monadic implicational subreducts, that is, the ${\{\rightarrow, \forall,1\}}$ -subreducts of the class of monadic MV-algebras. We prove that this class is an equational class, which we denote by ${\mathcal{ML}}$ , and we give an equational basis for this variety. An algebra in ${\mathcal{ML}}$ is called a monadic ?ukasiewicz implication algebra. We characterize the subdirectly irreducible members of ${\mathcal{ML}}$ and the congruences of every monadic ?ukasiewicz implication algebra by monadic filters. We prove that ${\mathcal{ML}}$ is generated by its finite members. Finally, we completely describe the lattice of subvarieties, and we give an equational basis for each proper subvariety.