GENERALIZED HIGHER DERIVATIONS

E. P. COJUHARI, B. J. GARDNER
2012 Bulletin of the Australian Mathematical Society  
A type of generalized higher derivation consisting of a collection of self-mappings of a ring associated with a monoid, and here called a D-structure, is studied. Such structures were previously used to define various kinds of 'skew' or 'twisted' monoid rings. We show how certain gradings by monoids define D-structures. The monoid ring defined by such a structure corresponding to a group-grading is the variant of the group ring introduced by Nȃstȃsescu, while in the case of a cyclic group of
more » ... cyclic group of order two, the form of the D-structure itself yields some gradability criteria of Bakhturin and Parmenter. A partial description is obtained of the D-structures associated with infinite cyclic monoids. 2010 Mathematics subject classification: primary 13N15, 16S36, 16A03; secondary 16W55.
doi:10.1017/s000497271100308x fatcat:ihw3b4u2yfbcrh7avmnbpbufue