When in a multiplicative derivation additive?
Our main objective in this note is to prove the following. Suppose R is a ring having an idempotent element e(e≠0, e≠1) which satisfies: (M1) xR=0 implies x=0.(M2) eRx=0 implies x=0 (and hence Rx=0 implies x=0).(M3) exeR(1−e)=0 implies exe=0. If d is any multiplicative derivation of...
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000844 |
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| _version_ | 1850219092552712192 |
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| author | Mohamad Nagy Daif |
| author_facet | Mohamad Nagy Daif |
| author_sort | Mohamad Nagy Daif |
| collection | DOAJ |
| description | Our main objective in this note is to prove the following. Suppose R is a
ring having an idempotent element e(e≠0, e≠1) which satisfies:
(M1) xR=0 implies x=0.(M2) eRx=0 implies x=0 (and hence Rx=0 implies x=0).(M3) exeR(1−e)=0 implies exe=0.
If d is any multiplicative derivation of R, then d is additive. |
| format | Article |
| id | doaj-art-78fef8de5da54a32a5df12619b22ba44 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-78fef8de5da54a32a5df12619b22ba442025-08-20T02:07:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114361561810.1155/S0161171291000844When in a multiplicative derivation additive?Mohamad Nagy Daif0Department of Mathematics, Faculty of Education, Umm Al-Qura University, Taif, Saudi ArabiaOur main objective in this note is to prove the following. Suppose R is a ring having an idempotent element e(e≠0, e≠1) which satisfies: (M1) xR=0 implies x=0.(M2) eRx=0 implies x=0 (and hence Rx=0 implies x=0).(M3) exeR(1−e)=0 implies exe=0. If d is any multiplicative derivation of R, then d is additive.http://dx.doi.org/10.1155/S0161171291000844ringidempotent elementderivationPeirce decomposition. |
| spellingShingle | Mohamad Nagy Daif When in a multiplicative derivation additive? International Journal of Mathematics and Mathematical Sciences ring idempotent element derivation Peirce decomposition. |
| title | When in a multiplicative derivation additive? |
| title_full | When in a multiplicative derivation additive? |
| title_fullStr | When in a multiplicative derivation additive? |
| title_full_unstemmed | When in a multiplicative derivation additive? |
| title_short | When in a multiplicative derivation additive? |
| title_sort | when in a multiplicative derivation additive |
| topic | ring idempotent element derivation Peirce decomposition. |
| url | http://dx.doi.org/10.1155/S0161171291000844 |
| work_keys_str_mv | AT mohamadnagydaif wheninamultiplicativederivationadditive |