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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171281000343 |
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| Summary: | 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 |
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| ISSN: | 0161-1712 1687-0425 |