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Generalized higher derivations
Citation
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
Abstract
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 |
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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 |
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