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Lie Ideals and Commutativity of Semiprime Rings with Generalized Derivation
Emine Koc Sogutcu,O ̈znur Go ̈lba ̧sı 영남수학회 2020 East Asian mathematical journal Vol.36 No.1
Inthispaper,weinvestigatecommutativityofsemiprimerings with a derivation which is strongly commutativity preserving and acts as a homomorphism or as an anti-homomorphism on a nonzero Lie ideal.
NOTES ON SYMMETRIC SKEW n-DERIVATION IN RINGS
Koc, Emine,Rehman, Nadeem ur Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.4
Let R be a prime ring (or semiprime ring) with center Z(R), I a nonzero ideal of R, T an automorphism of $R,S:R^n{\rightarrow}R$ be a symmetric skew n-derivation associated with the automorphism T and ${\Delta}$ is the trace of S. In this paper, we shall prove that S($x_1,{\ldots},x_n$) = 0 for all $x_1,{\ldots},x_n{\in}R$ if any one of the following holds: i) ${\Delta}(x)=0$, ii) [${\Delta}(x),T(x)]=0$ for all $x{\in}I$. Moreover, we prove that if $[{\Delta}(x),T(x)]{\in}Z(R)$ for all $x{\in}I$, then R is a commutative ring.
NOTES ON IDEALS AND ORTHOGONAL GENERALIZED ($\sigma$, $\tau$)-DERIVATIONS
Koc, Emine The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.4
In this paper, some results of [6] concerning orthogonal ($\sigma$, $\tau$)-derivations and generalized ($\sigma$, $\tau$)-derivations are generalized for a nonzero ideal of a semiprime ring.
Notes on ideals and orthogonal generalized (σ, τ )-derivations
Emine KOC 영남수학회 2008 East Asian mathematical journal Vol.24 No.4
In this paper, some results of [6] concerning orthogonal (σ, τ)-derivations and generalized (σ, τ)-derivations are generalized for a nonzero ideal of a semiprime ring.
LIE IDEALS AND COMMUTATIVITY OF 2-TORSION FREE SEMIPRIME RINGS WITH GENERALIZED DERIVATION
Sogutcu, Emine Koc,Golbasi, Oznur The Youngnam Mathematical Society 2020 East Asian mathematical journal Vol.36 No.1
In this paper, we investigate commutativity of semiprime rings with a derivation which is strongly commutativity preserving and acts as a homomorphism or as an anti-homomorphism on a nonzero Lie ideal.
The Westernization Process in Ottoman Women's Garments
Fatma KOC¸,Emine KOCA 이화여자대학교 아시아여성학센터 2007 Asian Journal of Women's Studies(AJWS) Vol.13 No.4
In Ottoman society, which maintained its tradition of clothing without change for a long time, the transformation of its dressing styles occurred via a long and protracted process. Westernization in Ottoman society started in the 17th and 18th Centuries, accompanied by attempts at modernizing and/or westernizing of fabrics, patterns, and colors. Along with the decrees of the administrative reforms, a process of westernization was put into motion. Changes in military costumes were undertaken and these then had an impact on civil costumes and clothing. Westernization in women?s attire underwent a slower process compared to that of men. Starting from the 17th Century till the formation of the Republic, women performed a silent but a decisive struggle relating to their concept of clothing. Westernization in a real sense for Turkish women came into practice in the era of the Republic of Turkey, founded by Kemal Ataturk. This study aims to discuss the process of westernization and the corresponding modifications that occurred in clothing in historical perspective.
ON (σ, τ)-LIE IDEALS WITH GENERALIZED DERIVATION
Oznur Golbasi,Emine Koc 대한수학회 2010 대한수학회보 Vol.47 No.6
In the present paper, we extend some well known results concerning derivations of prime rings to generalized derivations for (σ, τ)-Lie ideals.
ON (σ, τ)-LIE IDEALS WITH GENERALIZED DERIVATION
Golbasi, Oznur,Koc, Emine Korean Mathematical Society 2010 대한수학회보 Vol.47 No.6
In the present paper, we extend some well known results concerning derivations of prime rings to generalized derivations for ($\sigma,\tau$)-Lie ideals.
SOME COMMUTATIVITY THEOREMS OF PRIME RINGS WITH GENERALIZED (σ, τ)-DERIVATION
Golbasi, Oznur,Koc, Emine Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.3
In this paper, we extend some well known results concerning generalized derivations of prime rings to a generalized (${\sigma}$, ${\tau}$)-derivation.