Higher derivations on rings and modules
Let τ be a hereditary torsion theory on ModR and suppose that Qτ:ModR→ModR is the localization functor. It is shown that for all R-modules M, every higher derivation defined on M can be extended uniquely to a higher derivation defined on Qτ(M) if and only if τ is a higher differential torsion theory...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2373 |
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| _version_ | 1832560927003639808 |
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| author | Paul E. Bland |
| author_facet | Paul E. Bland |
| author_sort | Paul E. Bland |
| collection | DOAJ |
| description | Let τ be a hereditary torsion theory on ModR and suppose that Qτ:ModR→ModR is the localization functor. It is shown that for all R-modules M, every higher derivation defined on M can be extended uniquely to a higher derivation defined on Qτ(M) if and only if τ is a higher differential torsion theory. It is also shown that if τ is a TTF theory and Cτ:M→M is the colocalization functor, then a higher derivation defined on M can be lifted uniquely to a higher derivation defined on Cτ(M). |
| format | Article |
| id | doaj-art-1ddddc41526d4a7b9795405c0dfa317c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1ddddc41526d4a7b9795405c0dfa317c2025-02-03T01:26:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005152373238710.1155/IJMMS.2005.2373Higher derivations on rings and modulesPaul E. Bland0Department of Mathematics, Eastern Kentucky University, Richmond 40475, KY, USALet τ be a hereditary torsion theory on ModR and suppose that Qτ:ModR→ModR is the localization functor. It is shown that for all R-modules M, every higher derivation defined on M can be extended uniquely to a higher derivation defined on Qτ(M) if and only if τ is a higher differential torsion theory. It is also shown that if τ is a TTF theory and Cτ:M→M is the colocalization functor, then a higher derivation defined on M can be lifted uniquely to a higher derivation defined on Cτ(M).http://dx.doi.org/10.1155/IJMMS.2005.2373 |
| spellingShingle | Paul E. Bland Higher derivations on rings and modules International Journal of Mathematics and Mathematical Sciences |
| title | Higher derivations on rings and modules |
| title_full | Higher derivations on rings and modules |
| title_fullStr | Higher derivations on rings and modules |
| title_full_unstemmed | Higher derivations on rings and modules |
| title_short | Higher derivations on rings and modules |
| title_sort | higher derivations on rings and modules |
| url | http://dx.doi.org/10.1155/IJMMS.2005.2373 |
| work_keys_str_mv | AT paulebland higherderivationsonringsandmodules |