A System of Bi-Identities for Locally Inverse Semigroups

Abstract

Abstract. A class of regular semigroups closed under taking direct products, regular subsemigroups, and homomorphic images is an existence-variety (or evariety) of regular semigroups. Each e-variety of locally inverse semigroups can be characterized by a set of bi-identities. These are identities of terms of type (2, 2) in two sorts of variables X and X'. In this paper we obtain a basis of bi-identities for the e-variety of locally inverse semigroups and for certain sub-e-varieties.

Regular semigroups weakly generated by idempotents

“…This theory began in the 1990s [15,17] and a great effort was made on the development of a Birkhoff-type theorem for e-varieties of regular semigroups. Unfortunately, only partial results were found, namely for the e-varieties of locally inverse semigroups [1,2] and for the e-varieties of regular E-solid semigroups [18], and the interest on general e-varieties of regular semigroups diminished considerably. These partial results were based on the concepts of 'bifree objects' and 'biequational classes'.…”