MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS

Authors : E P COJUHARİ

Pages : 25-53

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Publication Date : 2007-12-01

Article Type : Research Paper

Abstract :We define on an arbitrary ring A a family of mappings insert ignore into journalissuearticles values(σx,y); subscripted with elements of a multiplicative monoid G. The assigned properties allow to call these mappings as derivations of the ring A. Beside the general situation it is given their description for the case of a partially ordered monoid. A monoid algebra of G over A is constructed explicitly, and the universality property of it is shown. The notion of a monoid algebra in our context extends those of a group ring, a skew polynomial ring, Weyl algebra and other related ones. The connection with crossed products is also shown.
Keywords : Derivations, monoid algebras, free algebras, skew polynomial rings