Commutative basic algebras and coupled near semirings

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• 作者：Ivan Chajda ; Helmut L?nger
• 关键词：Basic algebra ; Commutative basic algebra ; Near semiring ; Coupled near semiring
• 刊名：Soft Computing - A Fusion of Foundations, Methodologies and Applications
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：19
• 期：5
• 页码：1129-1134
• 全文大小：135 KB
• 参考文献：1. Belluce, LP, Nola, A, Ferraioli, AR (2013) MV-semirings and their sheaf representations. Order 30: pp. 165-179 CrossRef
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• 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

The relationship between MV-algebras and semirings was described by Di Nola and Gerla (Contemp Math 377:131-44, 2005). Since commutative basic algebras are similar to MV-algebras up to associativity of the binary operation we try to get a similar relationship between commutative basic algebras and so-called near semirings and we show that this is possible. This means that associativity does not play an important role in establishing a connection between an algebra of many-valued logic and a structure similar to a semiring.