A note on power invariant rings
Let R be a commutative ring with identity and R((n))=R[[X1,…,Xn]] the power series ring in n independent indeterminates X1,…,Xn over R. R is called power invariant if whenever S is a ring such that R[[X1]]≅S[[X1]], then R≅S. R is said to be forever-power-invariant if S is a ring and n is any positiv...
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Online Access: | http://dx.doi.org/10.1155/S0161171281000343 |
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doaj-82464845197e4bbfb3ee54c42f2a620b2020-11-24T21:19:52ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014348549110.1155/S0161171281000343A note on power invariant ringsJoong Ho Kim0Department of Mathematics, East Carolina University, Greenville 27834, N.C., USALet R be a commutative ring with identity and R((n))=R[[X1,…,Xn]] the power series ring in n independent indeterminates X1,…,Xn over R. R is called power invariant if whenever S is a ring such that R[[X1]]≅S[[X1]], 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 IC(R) denote the set of all a∈R such that there is R- homomorphism σ:R[[X]]→R with σ(X)=a. Then IC(R) is an ideal of R. It is shown that if IC(R) is nil, R is forever-power-invarianthttp://dx.doi.org/10.1155/S0161171281000343power series ringpower invariant ringforever-power-invariantideal-adic topology. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Joong Ho Kim |
spellingShingle |
Joong Ho Kim A note on power invariant rings International Journal of Mathematics and Mathematical Sciences power series ring power invariant ring forever-power-invariant ideal-adic topology. |
author_facet |
Joong Ho Kim |
author_sort |
Joong Ho Kim |
title |
A note on power invariant rings |
title_short |
A note on power invariant rings |
title_full |
A note on power invariant rings |
title_fullStr |
A note on power invariant rings |
title_full_unstemmed |
A note on power invariant rings |
title_sort |
note on power invariant rings |
publisher |
Hindawi Limited |
series |
International Journal of Mathematics and Mathematical Sciences |
issn |
0161-1712 1687-0425 |
publishDate |
1981-01-01 |
description |
Let R be a commutative ring with identity and R((n))=R[[X1,…,Xn]] the power series ring in n independent indeterminates X1,…,Xn over R. R is called power invariant if whenever S is a ring such that R[[X1]]≅S[[X1]], 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 IC(R) denote the set of all a∈R such that there is R- homomorphism σ:R[[X]]→R with σ(X)=a. Then IC(R) is an ideal of R. It is shown that if IC(R) is nil, R is forever-power-invariant |
topic |
power series ring power invariant ring forever-power-invariant ideal-adic topology. |
url |
http://dx.doi.org/10.1155/S0161171281000343 |
work_keys_str_mv |
AT joonghokim anoteonpowerinvariantrings AT joonghokim noteonpowerinvariantrings |
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1726004799713837056 |