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Generalized higher derivations
journal contribution
posted on 2023-05-17, 16:24 authored by Cojuhari, EP, Barry GardnerBarry GardnerA 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.
History
Publication title
Bulletin of the Australian Mathematical SocietyVolume
86Pagination
266-281ISSN
0004-9727Department/School
School of Natural SciencesPublisher
Australian Mathematics Publ Assoc IncPlace of publication
Mathematics Dept Australian National Univ, Canberra, Australia, Act, 0200Rights statement
Copyright 2012 Australian Mathematical Publishing Association Inc.Repository Status
- Restricted