Abstract
Proper extensions that are “injective on ℒ-related idempotents” of ℛ-unipotent semigroups, and much more generally of the class of generalised left restriction semigroups possessing the ample and congruence conditions, referred to here as glrac semigroups, are described as certain subalgebras of a λ-semidirect product of a left regular band by an ℛ-unipotent or by a glrac semigroup, respectively. An example of such is the generalized Szendrei expansion.
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