On Generalized Derivations and Commutativity of Associative Rings
Let be a ring with center Z(). A mapping f : → is said to be strong commutativity preserving (SCP) on if [f (x), f (y)] = [x, y] and is said to be strong anti-commutativity preserving (SACP) on if f (x) ◦ f (y) = x ◦ y for all x, y ∈. In the present paper, we apply the standard theory of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2020-06-01
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| Series: | Discussiones Mathematicae - General Algebra and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgaa.1330 |
| _version_ | 1797712883047464960 |
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| author | Sandhu Gurninder S. Kumar Deepak Davvaz Bijan |
| author_facet | Sandhu Gurninder S. Kumar Deepak Davvaz Bijan |
| author_sort | Sandhu Gurninder S. |
| collection | DOAJ |
| description | Let be a ring with center Z(). A mapping f : → is said to be strong commutativity preserving (SCP) on if [f (x), f (y)] = [x, y] and is said to be strong anti-commutativity preserving (SACP) on if f (x) ◦ f (y) = x ◦ y for all x, y ∈. In the present paper, we apply the standard theory of differential identities to characterize SCP and SACP derivations of prime and semiprime rings. |
| first_indexed | 2024-03-12T07:28:20Z |
| format | Article |
| id | doaj.art-89f7ca5c428f4b7885153729429a54aa |
| institution | Directory Open Access Journal |
| issn | 2084-0373 |
| language | English |
| last_indexed | 2024-03-12T07:28:20Z |
| publishDate | 2020-06-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae - General Algebra and Applications |
| spelling | doaj.art-89f7ca5c428f4b7885153729429a54aa2023-09-02T22:01:55ZengUniversity of Zielona GóraDiscussiones Mathematicae - General Algebra and Applications2084-03732020-06-01401496210.7151/dmgaa.1330dmgaa.1330On Generalized Derivations and Commutativity of Associative RingsSandhu Gurninder S.0Kumar Deepak1Davvaz Bijan2Department of Mathematics, Patel Memorial National College, Rajpura-140401, Punjab, IndiaDepartment of Mathematics, Punjabi University, Patiala-147002, Punjab, IndiaDepartment of Mathematics, Yazd University, Yazd, IranLet be a ring with center Z(). A mapping f : → is said to be strong commutativity preserving (SCP) on if [f (x), f (y)] = [x, y] and is said to be strong anti-commutativity preserving (SACP) on if f (x) ◦ f (y) = x ◦ y for all x, y ∈. In the present paper, we apply the standard theory of differential identities to characterize SCP and SACP derivations of prime and semiprime rings.https://doi.org/10.7151/dmgaa.1330generalized derivations(semi)prime ringsgeneralized polynomial identitiesmartindale ring of quotientsprimary 46j10, 16n20secondary 16n60, 16w25 |
| spellingShingle | Sandhu Gurninder S. Kumar Deepak Davvaz Bijan On Generalized Derivations and Commutativity of Associative Rings Discussiones Mathematicae - General Algebra and Applications generalized derivations (semi)prime rings generalized polynomial identities martindale ring of quotients primary 46j10, 16n20 secondary 16n60, 16w25 |
| title | On Generalized Derivations and Commutativity of Associative Rings |
| title_full | On Generalized Derivations and Commutativity of Associative Rings |
| title_fullStr | On Generalized Derivations and Commutativity of Associative Rings |
| title_full_unstemmed | On Generalized Derivations and Commutativity of Associative Rings |
| title_short | On Generalized Derivations and Commutativity of Associative Rings |
| title_sort | on generalized derivations and commutativity of associative rings |
| topic | generalized derivations (semi)prime rings generalized polynomial identities martindale ring of quotients primary 46j10, 16n20 secondary 16n60, 16w25 |
| url | https://doi.org/10.7151/dmgaa.1330 |
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