Commutative basic algebras and coupled near semirings

Abstract

The relationship between MV-algebras and semirings was described by Di Nola and Gerla (Contemp Math 377:131---144, 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.