Characterization of regular medial algebras

Amir Ehsani

ABSTRACT: In this paper we consider the algebra (A,f,g), where f and g are m-ary and n-ary operations on the set A. We define the concept of regular algebra and we prove that for a regular medial algebra (A,f,g) there exists a commutative semigroup (A,+) such that the operations f and g have linear representations on (A,+). As a corollary, we show that for a regular medial algebra (A,F) there exists a commutative semigroup (A,+) such that any operation f∈F has a linear representation on (A,+).

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Department of Mathematics, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran

* Corresponding author, E-mail: a.ehsani@mhriau.ac.ir

Received 2 Jun 2013, Accepted 3 Feb 2014