Abstract
UDC 512.64 Let be a vector space and let denote the semigroup (under composition) of all linear transformations from into . For a fixed subspace of , let be the semigroup consisting of all linear transformations from into . It is known that is the largest regular subsemigroup of . In this paper, we prove that any regular semigroup can be embedded in with and , and determine all the maximal subsemigroups of when is a finite dimensional subspace of over a finite field.
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