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ON A LIE RING OF GENERALIZED INNER DERIVATIONS
Aydin, Neset,Turkmen, Selin Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.4
In this paper, we define a set including of all $f_a$ with $a{\in}R$ generalized derivations of R and is denoted by $f_R$. It is proved that (i) the mapping $g:L(R){\rightarrow}f_R$ given by g (a) = f-a for all $a{\in}R$ is a Lie epimorphism with kernel $N_{{\sigma},{\tau}}$ ; (ii) if R is a semiprime ring and ${\sigma}$ is an epimorphism of R, the mapping $h:f_R{\rightarrow}I(R)$ given by $h(f_a)=i_{{\sigma}(-a)}$ is a Lie epimorphism with kernel $l(f_R)$ ; (iii) if $f_R$ is a prime Lie ring and A, B are Lie ideals of R, then $[f_A,f_B]=(0)$ implies that either $f_A=(0)$ or $f_B=(0)$.
Asar, Neset Volkan,Albayrak, Hamdi,Korkmaz, Turan,Turkyilmaz, Ilser The Korean Academy of Prosthodonitics 2013 The Journal of Advanced Prosthodontics Vol.5 No.3
PURPOSE. To evaluate the effect of various metal oxides on impact strength (IS), fracture toughness (FT), water sorption (WSP) and solubility (WSL) of heat-cured acrylic resin. MATERIALS AND METHODS. Fifty acrylic resin specimens were fabricated for each test and divided into five groups. Group 1 was the control group and Group 2, 3, 4 and 5 (test groups) included a mixture of 1% $TiO_2$ and 1% $ZrO_2$, 2% $Al_2O_3$, 2% $TiO_2$, and 2% $ZrO_2$ by volume, respectively. Rectangular unnotched specimens ($50mm{\times}6.0mm{\times}4.0mm$) were fabricated and drop-tower impact testing machine was used to determine IS. For FT, compact test specimens were fabricated and tests were done with a universal testing machine with a cross-head speed of 5 mm/min. For WSP and WSL, disc-shaped specimens were fabricated and tests were performed in accordance to ISO 1567. ANOVA and Kruskal-Wallis tests were used for statistical analyses. RESULTS. IS and FT values were significantly higher and WSP and WSL values were significantly lower in test groups than in control group (P<.05). Group 5 had significantly higher IS and FT values and significantly lower WSP values than other groups (P<.05) and provided 40% and 30% increase in IS and FT, respectively, compared to control group. Significantly lower WSL values were detected for Group 2 and 5 (P<.05). CONCLUSION. Modification of heat-cured acrylic resin with metal oxides, especially with $ZrO_2$, may be useful in preventing denture fractures and undesirable physical changes resulting from oral fluids clinically.
A REMARK ON THE CONJUGATION IN THE STEENROD ALGEBRA
TURGAY, NESET DENIZ Korean Mathematical Society 2015 대한수학회논문집 Vol.30 No.3
We investigate the Hopf algebra conjugation, ${\chi}$, of the mod 2 Steenrod algebra, $\mathcal{A}_2$, in terms of the Hopf algebra conjugation, ${\chi}^{\prime}$, of the mod 2 Leibniz-Hopf algebra. We also investigate the fixed points of $\mathcal{A}_2$ under ${\chi}$ and their relationship to the invariants under ${\chi}^{\prime}$.
THE SOURCE OF SEMIPRIMENESS OF RINGS
Aydin, Neset,Demir, Cagri,Camci, Didem Karalarlioglu Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.4
Let R be an associative ring. We define a subset $S_R$ of R as $S_R=\{a{\in}R{\mid}aRa=(0)\}$ and call it the source of semiprimeness of R. We first examine some basic properties of the subset $S_R$ in any ring R, and then define the notions such as R being a ${\mid}S_R{\mid}$-reduced ring, a ${\mid}S_R{\mid}$-domain and a ${\mid}S_R{\mid}$-division ring which are slight generalizations of their classical versions. Beside others, we for instance prove that a finite ${\mid}S_R{\mid}$-domain is necessarily unitary, and is in fact a ${\mid}S_R{\mid}$-division ring. However, we provide an example showing that a finite ${\mid}S_R{\mid}$-division ring does not need to be commutative. All possible values for characteristics of unitary ${\mid}S_R{\mid}$-reduced rings and ${\mid}S_R{\mid}$-domains are also determined.
SOME RESULTS ON GENERALIZED LIE IDEALS WITH DERIVATION
Aydin, Neset,Kaya, Kazim,Golbasi, Oznur The Youngnam Mathematical Society Korea 2001 East Asian mathematical journal Vol.17 No.2
Let R be a prime ring with characteristic not two. U a (${\sigma},{\tau}$)-left Lie ideal of R and d : R$\rightarrow$R a non-zero derivation. The purpose of this paper is to invesitigate identities satisfied on prime rings. We prove the following results: (1) [d(R),a]=0$\Leftrightarrow$d([R,a])=0. (2) if $(R,a)_{{\sigma},{\tau}}$=0 then $a{\in}Z$. (3) if $(R,a)_{{\sigma},{\tau}}{\subset}C_{{\sigma},{\tau}}$ then $a{\in}Z$. (4) if $(U,a){\subset}Z$ then $a^2{\in}Z\;or\;{\sigma}(u)+{\tau}(u){\in}Z$, for all $u{\in}U$. (5) if $(U,R)_{{\sigma},{\tau}}{\subset}C_{{\sigma},{\tau}}$ then $U{\subset}Z$.
SOME RESULTS ON ENDOMORPHISMS OF PRIME RING WHICH ARE $(\sigma,\tau)$-DERIVATION
Golbasi, Oznur,Aydin, Neset The Youngnam Mathematical Society Korea 2002 East Asian mathematical journal Vol.18 No.2
Let R be a prime ring with characteristic not two and U is a nonzero left ideal of R which contains no nonzero nilpotent right ideal as a ring. For a $(\sigma,\tau)$-derivation d : R$\rightarrow$R, we prove the following results: (1) If d is an endomorphism on R then d=0. (2) If d is an anti-endomorphism on R then d=0. (3) If d(xy)=d(yx), for all x, y$\in$R then R is commutative. (4) If d is an homomorphism or anti-homomorphism on U then d=0.
ON LIE IDEALS OF PRIME RINGS WITH GENERALIZED JORDAN DERIVATION
Golbasi, Oznur,Aydin, Neset The Youngnam Mathematical Society Korea 2005 East Asian mathematical journal Vol.21 No.1
The purpose of this paper is to show that every generalized Jordan derivation of prime ring with characteristic not two is a generalized derivation on a nonzero Lie ideal U of R such that $u^2{\in}U\;for\;{\forall}u{\in}U$ which is a generalization of the well-known result of I. N. Herstein.
Turan Korkmaz,Hai Albayrak,Ilser Turkyilmaz,Neset Volkan Asar 대한치과보철학회 2013 The Journal of Advanced Prosthodontics Vol.5 No.3
PURPOSE To evaluate the effect of various metal oxides on impact strength (IS), fracture toughness (FT), water sorption (WSP) and solubility (WSL) of heat-cured acrylic resin. MATERIALS AND METHODS Fifty acrylic resin specimens were fabricated for each test and divided into five groups. Group 1 was the control group and Group 2, 3, 4 and 5 (test groups) included a mixture of 1% TiO2 and 1% ZrO2, 2% Al2O3, 2% TiO2, and 2% ZrO2 by volume, respectively. Rectangular unnotched specimens (50 mm × 6.0 mm × 4.0 mm) were fabricated and droptower impact testing machine was used to determine IS. For FT, compact test specimens were fabricated and tests were done with a universal testing machine with a cross-head speed of 5 mm/min. For WSP and WSL, discshaped specimens were fabricated and tests were performed in accordance to ISO 1567. ANOVA and Kruskal-Wallis tests were used for statistical analyses. RESULTS IS and FT values were significantly higher and WSP and WSL values were significantly lower in test groups than in control group (P<.05). Group 5 had significantly higher IS and FT values and significantly lower WSP values than other groups (P<.05) and provided 40% and 30% increase in IS and FT, respectively, compared to control group. Significantly lower WSL values were detected for Group 2 and 5 (P<.05). CONCLUSION Modification of heat-cured acrylic resin with metal oxides, especially with ZrO2, may be useful in preventing denture fractures and undesirable physical changes resulting from oral fluids clinically.
Al Hwaeer, Hassan J.,Albkwre, Gbrel,Turgay, Neset Deniz Department of Mathematics 2020 Kyungpook mathematical journal Vol.60 No.2
In the proof of Theorem 3 on p.253 in [4], both right and left distributivity are assumed simultaneously which makes the proof invalid. We give a corrected proof for this theorem by introducing an extension of Lemma 2.2 in [2].