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 obtaine...
