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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 Nastasescu, while in the case of a 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.

Item Type:	Refereed Article
Keywords:	derivation, higher derivation, graded ring, monoid algebra
Research Division:	Mathematical Sciences
Research Group:	Pure mathematics
Research Field:	Algebra and number theory
Objective Division:	Expanding Knowledge
Objective Group:	Expanding knowledge
Objective Field:	Expanding knowledge in the mathematical sciences
UTAS Author:	Gardner, BJ (Dr Barry Gardner)
ID Code:	83133
Year Published:	2012
Web of Science® Times Cited:	2
Deposited By:	Mathematics and Physics
Deposited On:	2013-03-01
Last Modified:	2017-11-01
Downloads:	0