High Quality Content by WIKIPEDIA articles! In mathematics, an algebra is unital (some authors say unitary) if it contains a multiplicative identity element (or unit), i.e. an element 1 with the property 1x = x1 = x for all elements x of the algebra. Most associative algebras considered in abstract algebra, for instance group algebras, polynomial algebras and matrix algebras, are unital, if rings are assumed to be so. Most algebras of functions considered in analysis are not unital, for instance the algebra of functions decreasing to zero at infinity, especially those with compact support on some (non-compact) space. Given two unital algebras A and B, an algebra homomorphism f : A ? B is unital if it maps the identity element of A to the identity element of B. If the associative algebra A over the field K is not unital, one can adjoin an identity element as follows: take AxK as underlying K-vector space and define multiplication * by (x,r) * (y,s) = (xy + sx + ry, rs) for x,y in A and r,s in K. Then * is an associative operation with identity element (0,1).

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.