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GENERALIZED HIGHER DERIVATIONS

Part of: Rings and algebras arising under various constructions Differential algebra

Published online by Cambridge University Press:  06 January 2012

E. P. COJUHARI  and
B. J. GARDNER
E. P. COJUHARI*
Affiliation:
Department of Mathematics, Technical University of Moldova, Ştefan cel Mare av. 168, Chişinău, MD-2004, Moldova (email: ecojuhari@yahoo.com)
B. J. GARDNER
Affiliation:
Discipline of Mathematics, University of Tasmania, Private Bag 37, Hobart, Tas. 7001, Australia (email: gardner@hilbert.maths.utas.edu.au)
*
✉For correspondence; e-mail: ecojuhari@yahoo.com
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Abstract

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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 Năstăsescu, 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.

Keywords

derivationhigher derivationgraded ringmonoid algebra

MSC classification

Secondary: 13N15: Derivations 16S36: Ordinary and skew polynomial rings and semigroup rings
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 2 , October 2012 , pp. 266 - 281
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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