Abstract. The relationship between MV-algebras and semirings was described by A. Di Nola and B. Gerla in [DG] and [Ge]. An analogous result was proved by the authors for commutative basic algebras and so-called near semirings in [CL]. In order to generalize this approach to non-commutative basic algebras, we introduce the concept of right near semirings and point out some of their basic properties. We obtain a representation of basic algebras by so-called coupled right near semirings in a way similar to that obtained in [CL].
DOI: 10.14232/actasm-014-307-z
AMS Subject Classification
(1991): 03G25, 06D35, 16Y30, 16Y60
Keyword(s):
basic algebra,
right near semiring,
coupled right near semiring,
monotonous basic algebra,
weakly monotonous basic algebra
Received July 18, 2014, and in final form January 5, 2015. (Registered under 57/2014.)
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