On Regular Co-Medial Algebras

Amir Ehsani

Abstract


In this paper we define the concepts of co-medial algebra and  regular algebra and we will show that for a regular co-medial algebra $(A,f,g)$, there exist a commutative semigroup $(A,+)$, such that the operations $f,g$ have the linear representation on $(A,+)$. As a consequence of above result, we have the linear representation of an $n-$ary medial groupoid with an regular element, which was obtained by (Evans, T., 1963, p. 331-349).


Full Text: PDF DOI: 10.5539/jmr.v4n2p101

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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