In Billhardt et al. (Semigroup Forum 79:101–118, 2009) the authors introduced the notion of an associate inverse subsemigroup of a regular semigroup, extending the concept of an associate subgroup of a regular semigroup, first presented in Blyth et al. (Glasg. Math. J. 36:163–171, 1994). The semigroups of these two classes admit axiomatic characterisations in terms of unary operations and can, therefore, be considered as unary semigroups. In this paper we introduce the notion of unary semigroup with associate inverse subsemigroup [with associate subgroup] and show that the classes of such unary semigroups form varieties.
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机译：在Billhardt等人中。 （Semigroup Forum 79：101–118，2009）作者介绍了正则半群的准逆子半群的概念，扩展了正则半群的准子群的概念，最早在Blyth等人中提出。 （Glasg.Math.J.36：163-171，1994）。这两个类别的半群接受一元运算的公理化特征，因此可以视为一元半群。在本文中，我们介绍了具有关联逆子半群[具有关联子群]的一元半群的概念，并表明此类一元半群的类形成了变体。
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