MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS

We define on an arbitrary ring A a family of mappings (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,

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Department of Mathematical Modelling and Economical Informatics, State University of Moldova, str. A. Mateevici 60, MD-2009, Chisinau, Moldova
E-mail: cojuhari@usm.md