Involutive right-residuated l-groupoids

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• 作者：Ivan Chajda ; Sándor Radeleczki
• 关键词：Right ; residuated l ; groupoid ; Residuated lattice ; Antitone involution ; MV ; algebra ; Basic algebra ; Congruence regularity ; Primary 08B05 ; 03G25 ; Secondary 06B05 ; 06D15
• 刊名：Soft Computing - A Fusion of Foundations, Methodologies and Applications
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：20
• 期：1
• 页码：119-131
• 全文大小：508 KB
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• 作者单位：Ivan Chajda (1)
  Sándor Radeleczki (2)
  
  1. Department of Algebra and Geometry, Palacky University, 17. listopadu 12, Olomouc, 771 46, Czech Republic
  2. Mathematical Institute, University of Miskolc, 3515, Miskolc-Egyetemvaros, Hungary
  
• 刊物类别：Engineering
• 刊物主题：Numerical and Computational Methods in Engineering
  Theory of Computation
  Computing Methodologies
  Mathematical Logic and Foundations
  Control Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1433-7479

文摘

A common generalization of orthomodular lattices and residuated lattices is provided corresponding to bounded lattices with an involution and sectionally extensive mappings. It turns out that such a generalization can be based on integral right-residuated l-groupoids. This general framework is applied to MV-algebras, orthomodular lattices, Nelson algebras, basic algebras and Heyting algebras. Keywords Right-residuated l-groupoid Residuated lattice Antitone involution MV-algebra Basic algebra Congruence regularity