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Subnormalizing extensions and D-structures

Citation

Cojuhari, EP and Gardner, BJ, Subnormalizing extensions and D-structures, ROMAI Journal, 14, (2) pp. 59-66. ISSN 1841-5512 (2018) [Refereed Article]

Copyright Statement

Copyright 2018 Romanian Society of Applied & Industrial Mathematics

Abstract

If S is a subnormalizing extension [7] of a ring R with identity generated by a set which is a multiplicative submonoid of S and generates S as a free unital left R-module, then using the left and right module structures of S one can define a set of mappings RR which satisfy all but (possibly) one of the requirements for a D-structure [2], [3], [4]. It remains unknown whether this remaining condition must in fact be satisfied, but we show that it is satisfied for a number of particular monoids and is at least partially satisfied in general. In the other direction it is known that many but by no means all D-structures are linked to subnormalizing extensions in this way.

Item Details

Item Type:Refereed Article
Keywords:skew polynomial ring, skew monoid ring, subnormalizing extension, higher derivation, monoids
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:145786
Year Published:2018
Deposited By:Mathematics
Deposited On:2021-08-05
Last Modified:2021-09-16
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