On prime and semiprime rings with derivations
| dc.contributor.author | Argac, N | |
| dc.date.accessioned | 2019-10-27T19:17:21Z | |
| dc.date.available | 2019-10-27T19:17:21Z | |
| dc.date.issued | 2006 | |
| dc.department | Ege Üniversitesi | en_US |
| dc.description.abstract | Let R be a ring and S a nonempty subset of R. A mapping f : R --> R is called commuting on S if [f (x), x] = 0 for all x is an element of S. In this paper, firstly, we generalize the well-known result of Posner related to commuting derivations on prime rings. Secondly, we show that if R is a semiprime ring and I is a nonzero ideal of R, then a derivation d of R is commuting on I if one of the following conditions holds: (i) For all x, y is an element of I, either d([x, y]) = [x, y] or d([x, y]) = - [x, y]. (ii) For all x, y is an element of I, either d(x circle y) = x circle y or d(x circle y) = - (x circle y). (iii) R is 2-torsion free, and for all x, Y is an element of I, either [d(x), d(y)] = d([x, y]) or [d(x), d(y)] = d([y, x]). Furthermore, if d(I) not equal {0}, then R has a nonzero central ideal. Finally, we introduce the notation of generalized biderivation and prove that every generalized biderivation. on a noncommutative prime ring is a biderivation. | en_US |
| dc.identifier.doi | 10.1142/S1005386706000320 | |
| dc.identifier.endpage | 380 | en_US |
| dc.identifier.issn | 1005-3867 | |
| dc.identifier.issn | 1005-3867 | en_US |
| dc.identifier.issue | 3 | en_US |
| dc.identifier.scopusquality | Q3 | en_US |
| dc.identifier.startpage | 371 | en_US |
| dc.identifier.uri | https://doi.org/10.1142/S1005386706000320 | |
| dc.identifier.uri | https://hdl.handle.net/11454/38357 | |
| dc.identifier.volume | 13 | en_US |
| dc.identifier.wos | WOS:000238625200002 | en_US |
| dc.identifier.wosquality | Q4 | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | World Scientific Publ Co Pte Ltd | en_US |
| dc.relation.ispartof | Algebra Colloquium | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | (semi)prime ring | en_US |
| dc.subject | commuting mapping | en_US |
| dc.subject | centralizing mapping | en_US |
| dc.subject | derivation | en_US |
| dc.subject | generalized (bi)derivation | en_US |
| dc.title | On prime and semiprime rings with derivations | en_US |
| dc.type | Article | en_US |
