Baer extensions of rings and Stone extensions of semigroups.
Completely regular semigroups equipped with the unary operation of inversion within their maximal subgroups form a variety, denoted by . The lattice of subvarieties of is denoted by . For each variety in an -subsemilattice of , 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 , we construct -classes of all varieties in . Two figures illustrate...
In the present paper, we will show that the set of minimal elements of a full affine semigroup contains a free basis of the group generated by in . This will be applied to the study of the group for a semilocal ring .