Coefficient subrings of certain local rings with prime-power characteristic
If R is a local ring whose radical J(R) is nilpotent and R/J(R) is a commutative field which is algebraic over GF(p), then R has at least one subring S such that S=∪i=1∞Si, where each Si, is isomorphic to a Galois ring and S/J(S) is naturally isomorphic to R/J(R). Such subrings of R are mutually iso...
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| Format: | Article |
| Language: | English |
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Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171295000573 |
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| _version_ | 1850158323691683840 |
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| author | Takao Sumiyama |
| author_facet | Takao Sumiyama |
| author_sort | Takao Sumiyama |
| collection | DOAJ |
| description | If R is a local ring whose radical J(R) is nilpotent and R/J(R) is a commutative field
which is algebraic over GF(p), then R has at least one subring S such that S=∪i=1∞Si, where each Si, is
isomorphic to a Galois ring and S/J(S) is naturally isomorphic to R/J(R). Such subrings of R are mutually
isomorphic, but not necessarily conjugate in R. |
| format | Article |
| id | doaj-art-69f9c091c75c4cd49ae25816ce93bdce |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-69f9c091c75c4cd49ae25816ce93bdce2025-08-20T02:23:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118345146210.1155/S0161171295000573Coefficient subrings of certain local rings with prime-power characteristicTakao Sumiyama0Department of Mathematics, Aichi Institute of Technology, Yakusa-ch6, Toyota 470-03, JapanIf R is a local ring whose radical J(R) is nilpotent and R/J(R) is a commutative field which is algebraic over GF(p), then R has at least one subring S such that S=∪i=1∞Si, where each Si, is isomorphic to a Galois ring and S/J(S) is naturally isomorphic to R/J(R). Such subrings of R are mutually isomorphic, but not necessarily conjugate in R.http://dx.doi.org/10.1155/S0161171295000573coefficient ringGalois ringlocal ringSzele matrix. |
| spellingShingle | Takao Sumiyama Coefficient subrings of certain local rings with prime-power characteristic International Journal of Mathematics and Mathematical Sciences coefficient ring Galois ring local ring Szele matrix. |
| title | Coefficient subrings of certain local rings with prime-power characteristic |
| title_full | Coefficient subrings of certain local rings with prime-power characteristic |
| title_fullStr | Coefficient subrings of certain local rings with prime-power characteristic |
| title_full_unstemmed | Coefficient subrings of certain local rings with prime-power characteristic |
| title_short | Coefficient subrings of certain local rings with prime-power characteristic |
| title_sort | coefficient subrings of certain local rings with prime power characteristic |
| topic | coefficient ring Galois ring local ring Szele matrix. |
| url | http://dx.doi.org/10.1155/S0161171295000573 |
| work_keys_str_mv | AT takaosumiyama coefficientsubringsofcertainlocalringswithprimepowercharacteristic |