E-free objects and E-locality for completely regular semigroups.
Embedding semigroups in groups. A geometrical approach.
Embedding sums of cancellative modes into semimodules
A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice.
Equations on the semidirect product of a finite semilattice by a finite commutative monoid.