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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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171281000343 |
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| _version_ | 1832556826893221888 |
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| author | Joong Ho Kim |
| author_facet | Joong Ho Kim |
| author_sort | Joong Ho Kim |
| collection | DOAJ |
| 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 |
| format | Article |
| id | doaj-art-82464845197e4bbfb3ee54c42f2a620b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-82464845197e4bbfb3ee54c42f2a620b2025-02-03T05:44:16ZengWileyInternational 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. |
| 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. |
| title | 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_short | A note on power invariant rings |
| title_sort | note on power invariant rings |
| 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 |