Ringtheoretic properties of commutative algebras of invariants
(2003) In Journal of Algebra 266(1). p.239260 Abstract
 The commutative algebra of invariants of a Lie superalgebra 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 superalgebra 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
 00218693
 DOI
 10.1016/S00218693(03)001509
 language
 English
 LU publication?
 yes
 id
 5da1f522a240402c9e11044e3b601d86 (old id 305021)
 date added to LUP
 20160401 11:57:41
 date last changed
 20210217 04:12:57
@article{5da1f522a240402c9e11044e3b601d86, abstract = {The commutative algebra of invariants of a Lie superalgebra 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 = {00218693}, language = {eng}, number = {1}, pages = {239260}, publisher = {Elsevier}, series = {Journal of Algebra}, title = {Ringtheoretic properties of commutative algebras of invariants}, url = {http://dx.doi.org/10.1016/S00218693(03)001509}, doi = {10.1016/S00218693(03)001509}, volume = {266}, year = {2003}, }