Bavula, V.V. orcid.org/0000-0003-2450-2075 (2024) Inner generalized Weyl algebras and their simplicity criteria. Journal of Algebra and Its Applications, 23 (13). 2450218. ISSN 0219-4988
Abstract
The aim of the paper is to introduce a new class of rings — the inner generalized Weyl algebras (IGWA) — and to give simplicity criteria for them. For each IGWA A a derivative series of IGWAs, A→A′→A′′→⋯→A(α)→⋯, is attached where α is an arbitrary ordinal. In general, all rings A(α) are distinct. A new construction of rings, the inner(σ,τ,a)-extension of a ring, is introduced (where σ and τ are endomorphisms of a ring D and a∈D).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 The Author(s). This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 (CC BY-NC) License which permits use, distribution and reproduction in any medium, provided that the original work is properly cited and is used for non-commercial purposes. https://creativecommons.org/licenses/by-nc/4.0/ |
Keywords: | Generalized Weyl algebra; inner generalized Weyl algebra; simplicity criterion; normal element; defining relations; grading; endomorphism; automorphism; regular element; centre; fixed ring; ideal; module |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 09 Jan 2024 09:37 |
Last Modified: | 13 Mar 2025 23:39 |
Status: | Published |
Publisher: | World Scientific Pub Co Pte Ltd |
Refereed: | Yes |
Identification Number: | 10.1142/s0219498824502189 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:207319 |