Ring-theoretic properties of commutative algebras of invariants
(2003) In Journal of Algebra 266(1). p.239-260- Abstract
- The commutative algebra of invariants of a Lie super-algebra need not be affine, but does have a common ideal with an affine algebra, in all the known examples. This leads us to extend a class of algebras C to a class which we call "nearly C", by admitting those algebras C having a common ideal A with an algebra (containing C) in C such that C/A is an element of C. We generalize this notion slightly. study the prime ideals of such algebras, and extend some of the standard theorems about affine algebras, Noetherian rings, and Dedekind domains. Our main theorem is that nearly affine domains are catenary, and the Krull dimension equals the transcendence degree of the quotient field. Nevertheless, it is known that nearly affine domains need... (More)
- The commutative algebra of invariants of a Lie super-algebra need not be affine, but does have a common ideal with an affine algebra, in all the known examples. This leads us to extend a class of algebras C to a class which we call "nearly C", by admitting those algebras C having a common ideal A with an algebra (containing C) in C such that C/A is an element of C. We generalize this notion slightly. study the prime ideals of such algebras, and extend some of the standard theorems about affine algebras, Noetherian rings, and Dedekind domains. Our main theorem is that nearly affine domains are catenary, and the Krull dimension equals the transcendence degree of the quotient field. Nevertheless, it is known that nearly affine domains need not be Mori. (C) 2003 Elsevier Inc. All rights reserved. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/305021
- author
- Kantor, Isaiah LU and Rowen, L H
- organization
- publishing date
- 2003
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- catenary, complete integral closure, prime spectrum, Dedekind, nearly, nearly Noetherian, affine nearly affine, Noetherian
- in
- Journal of Algebra
- volume
- 266
- issue
- 1
- pages
- 239 - 260
- publisher
- Elsevier
- external identifiers
-
- wos:000184361100017
- scopus:0042659132
- ISSN
- 0021-8693
- DOI
- 10.1016/S0021-8693(03)00150-9
- language
- English
- LU publication?
- yes
- id
- 5da1f522-a240-402c-9e11-044e3b601d86 (old id 305021)
- date added to LUP
- 2016-04-01 11:57:41
- date last changed
- 2022-02-18 07:52:15
@article{5da1f522-a240-402c-9e11-044e3b601d86,
abstract = {{The commutative algebra of invariants of a Lie super-algebra need not be affine, but does have a common ideal with an affine algebra, in all the known examples. This leads us to extend a class of algebras C to a class which we call "nearly C", by admitting those algebras C having a common ideal A with an algebra (containing C) in C such that C/A is an element of C. We generalize this notion slightly. study the prime ideals of such algebras, and extend some of the standard theorems about affine algebras, Noetherian rings, and Dedekind domains. Our main theorem is that nearly affine domains are catenary, and the Krull dimension equals the transcendence degree of the quotient field. Nevertheless, it is known that nearly affine domains need not be Mori. (C) 2003 Elsevier Inc. All rights reserved.}},
author = {{Kantor, Isaiah and Rowen, L H}},
issn = {{0021-8693}},
keywords = {{catenary; complete integral closure; prime spectrum; Dedekind; nearly; nearly Noetherian; affine nearly affine; Noetherian}},
language = {{eng}},
number = {{1}},
pages = {{239--260}},
publisher = {{Elsevier}},
series = {{Journal of Algebra}},
title = {{Ring-theoretic properties of commutative algebras of invariants}},
url = {{http://dx.doi.org/10.1016/S0021-8693(03)00150-9}},
doi = {{10.1016/S0021-8693(03)00150-9}},
volume = {{266}},
year = {{2003}},
}