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Generalized higher derivations


Cojuhari, EP and Gardner, BJ, Generalized higher derivations, Bulletin of the Australian Mathematical Society, 86, (2) pp. 266-281. ISSN 0004-9727 (2012) [Refereed Article]

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Copyright Statement

Copyright 2012 Australian Mathematical Publishing Association Inc.

DOI: doi:10.1017/S000497271100308X


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 Details

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

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