Woods, Billy (2023) Dimension Theory in Iterated Local Skew Power Series Rings. Algebras and Representation Theory, 26 (5). pp. 1583-1608. DOI https://doi.org/10.1007/s10468-022-10144-3
Woods, Billy (2023) Dimension Theory in Iterated Local Skew Power Series Rings. Algebras and Representation Theory, 26 (5). pp. 1583-1608. DOI https://doi.org/10.1007/s10468-022-10144-3
Woods, Billy (2023) Dimension Theory in Iterated Local Skew Power Series Rings. Algebras and Representation Theory, 26 (5). pp. 1583-1608. DOI https://doi.org/10.1007/s10468-022-10144-3
Abstract
Many well-known local rings, including soluble Iwasawa algebras and certain completed quantum algebras, arise naturally as iterated skew power series rings. We calculate their Krull and global dimensions, obtaining lower bounds to complement the upper bounds obtained by Wang. In fact, we show that many common such rings obey a stronger property, which we call triangularity, and which allows us also to calculate their classical Krull dimension (prime length). Finally, we correct an error in the literature regarding the associated graded rings of general iterated skew power series rings, but show that triangularity is enough to recover this result.
Item Type: | Article |
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Uncontrolled Keywords: | Iwasawa algebras; Skew power series rings; Local rings; Quantum algebras |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 29 Jul 2022 14:02 |
Last Modified: | 16 May 2024 21:24 |
URI: | http://repository.essex.ac.uk/id/eprint/33206 |
Available files
Filename: Woods2022_Article_DimensionTheoryInIteratedLocal.pdf
Licence: Creative Commons: Attribution 3.0