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Subnormalizing extensions and D-structures
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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 R → R 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 Type: | Article |
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Authors/Creators: | Cojuhari, EP and Gardner, BJ |
Keywords: | skew polynomial ring, skew monoid ring, subnormalizing extension, higher derivation, monoids |
Journal or Publication Title: | ROMAI Journal |
Publisher: | Romanian Society of Applied and Industrial Mathematics |
ISSN: | 1841-5512 |
Copyright Information: | Copyright 2018 Romanian Society of Applied & Industrial Mathematics |
Item Statistics: | View statistics for this item |
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