dc.contributor.author | Muharrem Soytürk | |
dc.date.accessioned | 23.07.201910:49:13 | |
dc.date.accessioned | 2019-07-23T16:19:49Z | |
dc.date.available | 23.07.201910:49:13 | |
dc.date.available | 2019-07-23T16:19:49Z | |
dc.date.issued | 1996 | |
dc.identifier.issn | 1300-0098 | |
dc.identifier.uri | http://www.trdizin.gov.tr/publication/paper/detail/TXpjd09ETXo= | |
dc.identifier.uri | https://hdl.handle.net/20.500.12418/1039 | |
dc.description.abstract | R bir "halka, $X\neq(0)$ bir R-bi-modül, $U\neq(0)$, R'nin bir ideali $\sigma,\tau$ R nin iki otomorfizmi ve $d:R\rightarrow X d\sigma = \sigma d, d\tau = \tau d$ olacak şekilde bir modül değerli $(\sigma, \tau)$ türevi olsun. Ayrıca: $a\in R,x\in X$ ler için xRa=0 ise x=0 veya a=0 ...... $(G_1)$ aRx=0 ise a=0 veya x=0 ...... $(G_2)$ özellikleri bulunsun. Bu makalede aşağıdaki sonuçlar ispatlanmıştır. (1)$(G_ı)$ özelliği var ve d(U)a= 0 ise a = 0 veya d = 0 dır. (2)$(G_ı)$ özelliği var ve $[X,U]_{\sigma,\tau} \subset C_{\sigma,\tau}(X)$ ise R komütatiftir. (3)$(G_1)(G_2)$ özellikleri var olsun. $X\neq(0)$, 2-torsion-free R-bi-modül ve $a\in U[d(U),a]_{\sigma,\tau}\subset C_{\sigma,\tau}(X)$ ise $a\in Z$ veya d= 0. | en_US |
dc.description.abstract | Let R be a ring, $X\neq(0)$ an R-bi-module, $d:R\rightarrow X a(\sigma,\tau)$- derivation with module value such that $d\sigma=\sigma d, d\tau=\tau d$ and $U \neq(0)$ an ideal of R. Furthermore the following properties are also satisfied. For $x\in X, a\in R$ xRa=0 implies x=0 or a=0 ...... $(G_1)$ For $a\in R, x\in X$ aRx=0 implies a=0 or x=0 ...... $(G_2)$ In this paper we have proved the following results; (1) If $(G_1)$ (or $(G_2)$) is satisfied and for $a\in R$, d(U)a=0 (or ad(U)=0) then d=0 or a=0 (2) If $(G_1)$ is satisfied and $[X,U] \subset C(X)$ or $[X,U]_{\sigma,\tau}\subset C_{\sigma,\tau}(X)$ then R is commutative (3) Let X be a 2-torsion free R-bi module, $d_1:R \rightarrow Xa(\sigma,\tau)$ -derivation, $d_2:R\rightarrow R$ a derivation such that $d_2(U)\subset U$. If $(G_1)$ is satisfied and $d_1 d_2(U)=0$ then $d_1=0$ or $d_2=0$ (4) Let X be a 2-torsion free R-bi-module. If $(G_1)$ and $(G_2)$ are satisfied and for $ a\in U[d(U),a]_{\sigma,\tau}\subset C_{\sigma,\tau}(X)$ then $a\in Z$ or d=0. | en_US |
dc.language.iso | eng | en_US |
dc.rights | info:eu-repo/semantics/openAccess | en_US |
dc.subject | Matematik | en_US |
dc.title | On $(\sigma,\tau)$ derivations with module values | en_US |
dc.title.alternative | Modül değerli $(\sigma,\tau)$-türevler üzerine | en_US |
dc.type | other | en_US |
dc.relation.journal | Turkish Journal of Mathematics | en_US |
dc.contributor.department | Sivas Cumhuriyet Üniversitesi | en_US |
dc.identifier.volume | 20 | en_US |
dc.identifier.issue | 4 | en_US |
dc.identifier.endpage | 569 | en_US |
dc.identifier.startpage | 563 | en_US |
dc.relation.publicationcategory | Diğer | en_US] |