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Ring-theoretic properties of commutative algebras of invariants

Kantor, Isaiah LU and Rowen, L H (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)
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author
organization
publishing date
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
language
English
LU publication?
yes
id
5da1f522-a240-402c-9e11-044e3b601d86 (old id 305021)
date added to LUP
2007-09-13 15:30:36
date last changed
2018-05-29 11:28:50
@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},
  keyword      = {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/},
  volume       = {266},
  year         = {2003},
}