• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.23-34
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• 2005

Let R be a ring with left identity. Let G : $R{\times}R{\to}R$ be a symmetric biadditive mapping and g the trace of G. Let ${\alpha}\;:\;R{\to}R$ be an endomorphism and ${\beta}\;:\;R{\to}R$ an epimorphism. In this paper we show the following: (i) Let R be 2-torsion-free. If g is (${\alpha},{\beta}$)-skew-commuting on R, then we have G = 0. (ii) If g is (${\beta},{\beta}$)-skew-centralizing on R, then g is (${\beta},{\beta}$)-commuting on R. (iii) Let $n{\ge}2$. Let R be (n+1)!-torsion-free. If g is n-(${\alpha},{\beta}$)-skew-commuting on R, then we have G = 0. (iv) Let R be 6-torsion-free. If g is 2-(${\alpha},{\beta}$)-commuting on R, then g is (${\alpha},{\beta}$)-commuting on R.

• Nutrition Research and Practice
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• v.10 no.4
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• pp.377-384
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• 2016

BACKGROUND/OBJECTIVES: Resveratrol, a natural polyphenol, has multiple functions in cellular responses including apoptosis, survival, and differentiation. It also participates in the regulation of inflammatory response and oxidative stress. MicroRNA-Let-7A (miR-Let7A), known as a tumor suppressor miRNA, was recently reported to play a crucial role in both inflammation and apoptosis. Therefore, we examined involvement of miR-Let7A in the modulation of inflammation and cell survival/apoptosis regulated by resveratrol. MATERIALS/METHODS: mRNA expression of pro-/anti-inflammatory cytokines and sirtuin 1 (SIRT1), and protein expression of apoptosis signal-regulating kinase 1 (ASK1), p-ASK1, and caspase-3 and cleaved caspase-3 were measured, and cell viability and Hoechst/PI staining for apoptosis were observed in Lipopolysaccharide (LPS)-stimulated human THP-1 macrophages with the treatment of resveratrol and/or miR-Let7A overexpression. RESULTS: Pre-treatment with resveratrol ($25-200{\mu}M$) resulted in significant recovery of the reduced cell viabilities under LPS-induced inflammatory condition and in markedly increased expression of miR-Let7A in non-stimulated or LPS-stimulated cells. Increased mRNA levels of tumor necrosis $factor-{\alpha}$ and interleukin (IL)-6 induced by LPS were significantly attenuated, and decreased levels of IL-10 and brain-derived neurotrophic factor were significantly restored by resveratrol and miR-Let7A overexpression, respectively, or in combination. Decreased expression of IL-4 mRNA by LPS stimulation was also significantly increased by miR-Let7A overexpression co-treated with resveratrol. In addition, decreased SIRT1 mRNA levels, and increased p-ASK1 levels and PI-positive cells by LPS stimulation were significantly restored by resveratrol and miR-Let7A overexpression, respectively, or in combination. CONCLUSIONS: miR-Let7A may be involved in the inflammatory response and cell survival/apoptosis modulated by resveratrol in human THP-1 macrophages.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.783-796
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• 1994

Let V be a vector space of dimension m over Q, and let (, ) be a non-degenerate bilinear form on V. Let r be the Witt index of V, and let $V = V' + V_0 + V"$ be the Witt decomposition, where $V_0$ is anisotropic and V', V" are paired non-singularly. Let H = O(m-r, r) be the isometry group of V, (, ), viewed as an algebraic group over Q. Let G = Sp(n) be the symplectic group of rank n defined over Q.ed over Q.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.513-519
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• 2008

Let (R, m) be a Noetherian local ring with maximal ideal m, E := $E_R$(R/m) and let I be an ideal of R. Let M and N be finitely generated R-modules. It is shown that $H^n_I(M,(H^n_I(N)^{\vee})){\cong}(M{\otimes}_RN)^{\vee}$ where grade(I, N) = n = $cd_i$(I, N). We also show that for n = grade(I, R), one has $End_R(H^n_I(P,R)^{\vee}){\cong}Ext^n_R(H^n_I(P,R),P^*)^{\vee}$.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.75-85
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• 1992

Let R be an associative ring and let G be a finite group of Jordan automorphisms of R. Let $R^G$ be the set of elements in R fixed by all $g{\in}G$. In this paper we will study the relationship between the Levitzki radical of $R^G$ and R as that a Jordan ring. We also show that if R is a P.I. algebra, then the algebraicity of $R^G$ implies the algebraicity of R.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1221-1233
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• 2018

Let R be a commutative ring with non-zero identity and let NN(R) = {I | I is a nonnil ideal of R}. Let M be an R-module and let ${\phi}-tor(M)=\{x{\in}M{\mid}Ix=0\text{ for some }I{\in}NN(R)\}$. If ${\phi}or(M)=M$, then M is called a ${\phi}$-torsion module. An R-module M is said to be ${\phi}$-flat, if $0{\rightarrow}{A{\otimes}_R}\;{M{\rightarrow}B{\otimes}_R}\;{M{\rightarrow}C{\otimes}_R}\;M{\rightarrow}0$ is an exact R-sequence, for any exact sequence of R-modules $0{\rightarrow}A{\rightarrow}B{\rightarrow}C{\rightarrow}0$, where C is ${\phi}$-torsion. In this paper, the concepts of NRD-submodules and NP-submodules are introduced, and the ${\phi}$-flat modules over a ${\phi}-Pr{\ddot{u}}fer$ ring are investigated.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.365-376
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• 2006

Let R be a commutative ring and let M be an R-module. Let X = $Spec_R(M)$ be the prime spectrum of M with Zariski topology. In this paper, by using the topological properties of X, we will obtain some conditions under which $Max_R(M)=Spec_R(M)$.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.653-666
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• 2007

Let R be a commutative Noetherian ring (with a nonzero identity) and let M be an R-module. Further let I be an ideal of R. In this paper, by putting a suitable condition on $Ass_R$(M), we obtain some results concerning $I^{*(M)}$ and prove that the sequence of sets $Ass_R(R/(I^n)^{*(M)})$, $n\;\in\;N$, is increasing and ultimately constant. (Here $(I^n)^{*(M)}$ denotes the integral closure of $I^n$ relative to M.)

• Asian Pacific Journal of Cancer Prevention
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• v.17 no.4
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• pp.1887-1890
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• 2016

Breast cancer is the most common cause of cancer-related death among women in the whole world. MiR- 34a and let-7a are well known tumor suppressors that participate in the regulation of apoptosis, invasion and other cellular functions. In this study, expression of miR-34a, let-7a and apoptosis pathway genes such as Bcl-2, Caspase-3 and P53 were evaluated using quantitative real-time PCR in 45 paired samples of normal margin and tumor tissue collected from breast cancer patient at advanced stage (3-4). MiR-34a, let-7a, caspase-3 and P53 expression are reduced and Bcl-2 expression is increased within tumoral tissues in comparison with normal margin tissues. P53 expression directly or indirectly was correlated with miR-34a, let-7a, Bcl-2 and caspase-3 expression. In This study we found that MiR-34a and let-7a expression are reduced in the tumoral tissues. Down-regulation of these two molecules correlated with expression of genes associated with apoptosis. These results suggest that due to the correlation of miR-34a and let-7a with apoptotic and anti-apoptotic pathways these molecules could participate as regulators in advanced clinical stages of breast cancer and should be considered as markers for diagnosis, prognostic assessment and targeted therapy.