Note on cyclic doppelsemigroups

Abstract

A~doppelsemigroup \((G,\dashv,\vdash)\) is called cyclic if \((G,\dashv)\) is a~cyclic group. In the paper, we describe up to isomorphism all cyclic (strong) doppelsemigroups. We prove that up to isomorphism there exist \(\tau(n)\) finite cyclic (strong) doppelsemigroups of order \(n\), where \(\tau\) is the number of divisors function. Also there exist infinite countably many pairwise non-isomorphic infinite cyclic (strong) doppelsemigroups.