Our aim is to investigate the normalization (nilpotent shift) (RAr}* of the variety RAr of rectangular algebras of a finite type r. It can be regarded as a common generalization of various algebras studied by different authors, namely of rectangular algebras, [P&R 92, 93], rectangular bands, [Gou], medial grupoids, [J&K], or generalized diagonal algebras, [P 64, 66a, b]. We will determine all subdirectly irreducible algebras in the normalization of the variety of rectangular algebras, give a normal form for terms in the normalization and an algorithm for finding a subdirect decomposition of algberas belonging to the normalization.
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