High Quality Content by WIKIPEDIA articles! A non-associative algebra (or distributive algebra) over a field (or a ring) K is a K-vector space (or more generally a module) A equipped with a K-bilinear map A times A rightarrow A. There are left and right multiplication maps L_a : x mapsto ax and R_a : x mapsto xa. The enveloping algebra of A is the subalgebra of all K-endomorphisms of A generated by the multiplication maps.An algebra is unital or unitary if it has a unit or identity element I with Ix = x = xI for all x in the algebra.The best-known kinds of non-associative algebras are those that are nearly associative—that is, in which some simple equation constrains the differences between different ways of associating multiplication of elements.

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