A note on power invariant rings

Joong Ho Kim

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-7

Abstract:

Let R be a commutative ring with identity and R ( ( n ) ) = R [ [ X 1 , … , X n ] ] the power series ring in n independent indeterminates X 1 , … , X n over R . R is called power invariant if whenever S is a ring such that R [ [ X 1 ] ] ≅ S [ [ X 1 ] ] , then R ≅ S . R is said to be forever-power-invariant if S is a ring and n is any positive integer such that R ( ( n ) ) ≅ S ( ( n ) ) then R ≅ S Let I C ( R ) denote the set of all a ∈ R such that there is R - homomorphism σ : R [ [ X ] ] → R with σ ( X ) = a . Then I C ( R ) is an ideal of R . It is shown that if I C ( R ) is nil, R is forever-power-invariant

Date: 1981
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/4/372713.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/4/372713.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:372713

DOI: 10.1155/S0161171281000343

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().