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.)