ieja International Electronic Journal of Algebra 1306-6048 Abdullah HARMANCI MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS Cojuhari E. P. 12 01 2007 2 2 25 53 12 01 2007 Copyright © 2007, International Electronic Journal of Algebra 2007 International Electronic Journal of Algebra

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.

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