Abstract
For a given extension A⊂E of associative algebras we describe and classify up to an isomorphism all A-complements of E, i.e. all subalgebras X of E such that E=A+X and A∩X={0}. Let X be a given complement and (A,X,▹,◃,↼,⇀) the canonical matched pair associated with the factorization E=A+X. We introduce a new type of deformation of the algebra X by means of the given matched pair and prove that all A-complements of E are isomorphic to such a deformation of X. Several explicit examples involving the matrix algebra are provided.
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