Abstract: Completely regular semigroups equipped with the unary operation of inversion within their maximal subgroups form a variety, denoted by {CR}. The lattice of subvarieties of \,{CR} is denoted by \mathcal{L}({CR}). For each variety in an \bigcap-subsemilattice \Gamma of \mathcal{L}({CR}), we construct at least one basis of identities, and for some important varieties, several. We single out certain remarkable types of bases of general interest. As an application for the local relation L, we construct \mathbf{L}-classes of all varieties in \Gamma. Two figures illustrate the theory.
Keywords: semigroup; completely regular; variety; basis; local relation
DOI: DOI 10.14712/1213-7243.2021.005
AMS Subject Classification: 20M07 20M10