Artin theorem for semigroups

Abstract

In this paper, we prove an Artin type theorem for semigroups. Namely, we consider the concepts of hyperalternative and hyperassociative semigroups and prove that every two elements in any hyperalternative semigroup generate a hyperassociative subsemigroup. As a consequence, we characterize all hyperalternative semigroups, and prove that these semigroups form a variety of semigroups with four identities.