• 대한수학회논문집
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• 제33권1호
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• pp.103-125
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• 2018

Let R be a 5!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. Then $[D(x),x]D(x)^2=0$ if and only if $D(x)^2[D(x), x]=0$ for every $x{\in}R$. In particular, let A be a Banach algebra with rad(A) and if D is a continuous linear Jordan derivation on A, then we show that $[D(x),x]D(x)2{\in}rad(A)$ if and only if $D(x)^2[D(x),x]{\in}rad(A)$ for all $x{\in}A$ where rad(A) is the Jacobson radical of A.

• 호남수학학술지
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• 제41권3호
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• pp.531-538
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• 2019

We introduce FI-${\oplus}$-supplemented modules as a proper generalization of ${\oplus}$-supplemented modules. We prove that; (1) every finite direct sum of FI-${\oplus}$-supplemented R-modules is an FI-${\oplus}$-supplemented R-module for any ring R ; (2) if every left R-module is FI-${\oplus}$-supplemented over a semilocal ring R, then R is left perfect; (3) if M is a finitely generated torsion-free uniform R-module over a commutative integrally closed domain such that every direct summand of M is FI-${\oplus}$-supplemented, then M is a direct sum of cyclic modules.

• 충청수학회지
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• 제30권2호
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• pp.251-258
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• 2017

The aim of the present paper is to establish some results involving generalized ${\ast}$-derivations in ${\ast}$-rings and investigate the commutativity of prime ${\ast}$-rings admitting generalized ${\ast}$-derivations of R satisfying certain identities and some related results have also been discussed.

• 충청수학회지
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• 제30권3호
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• pp.313-321
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• 2017

In this paper, we introduce the notion of a ${\ast}$-semiderivation on ${\ast}$-rings, and we try to extend some results for derivations of rings or near-rings to a more general case for ${\ast}$-semiderivations of prime ${\ast}$-rings.

• 약학회지
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• 제36권6호
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• pp.518-528
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• 1992

To determine the optimal conformation of sulfonylureas, the correlation between conformation and hypoglycemic activity of the two sulfonylureas of tolbutamide and chlorpropamide as hypoglycemic agent was studied using an empirical potential function (ECEPP/2) and the hydration shell model in the unhydrated and hydrated states. The conformational energy was minimized from several starting conformations with possible torsion angles in each molecule. The conformational entropy change of each conformation was computed using a harmonic approximation. To understand the hydration effect on the conformation of the molecules in aqueous solution, the contribution of water-accessible volume of each group or atom in the lowest-free-energy conformation was calculated and compared each other. From comparison of the computed lowest-free-energy conformations of two sulfonylureas, it could be suggested that the hydration of sulfonylurea moiety is related to increase the hypoglycemic activity. From the calculation results, it was known that the conformational entropy is the major contribution to stabilize the low-free-energy conformations of two sulfonylureas in unhydrated state. Whereas, in hydrated state, the hydration free energy largely contributes to the total free energies of low-free-energy conformations of tolbutamide and conformational entropy contributes to stabilize the low-free-energy conformations of chlorpropamide. The torsion angles from phenyl ring to urea moiety of the low-free-energy conformations of the two sulfonylureas were shown the nearly regular trend. On the basis of these results, the conformation exhibiting the optimal hypoglycemic activity of sulfonylureas and the binding direction to pancreatic receptor site A could be predicted. Also, according to the side chain lengthening of urea moiety, tolbutamide showed various conformational change. Therefore, steric effect may be important factor in the interaction between sulfonylureas and the putative pancreatic receptor.

• 약학회지
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• 제39권3호
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• pp.329-336
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• 1995

Conformational free energy calculations using an empirical potential function and a hydration shell model(program CONBIO) were carried out on hypoglycemic agent acetohexamide and tolazamide in the unhydrated and hydrated states. The initial geometry of sulfonylureas was obtained from X-ray crystallographieal data and homologous molecular fragments. In both states, the feasible conformations were obtained from the calculations of conformational energy, conformational entropy, and hydration free energy by varying all the torsion angles of the molecules. From the calculation results, it is known that the conformations] entropy is the major contribution to stabflize the low-free-energy conformations of two sulfonylureas in both states. But, in hydrated state, the hydration does not directly affect each conformations. The intramolecular hydrogen bonding of sulfonylurea hydrogen and 7-membered nitrogen appeared to the conformations of tolazamide in both states. It is thought that the hydrogen bonding decrease steric hindrance on the receptor binding direction. The substitution of alicyclic or N-heterocyclic ring than that of carbons chain of urea moiety may be properly interaction between sulfonylureas and the putative pancreatic receptor.

• 충청수학회지
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• 제29권4호
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• pp.531-542
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• 2016

Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation $D:R{\rightarrow}R$ such that [[D(x),x], x]D(x) = 0 or D(x)[[D(x), x], x] = 0 for all $x{\in}R$. In this case we have $[D(x),x]^3=0$ for all $x{\in}R$. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A{\rightarrow}A$ such that $[[D(x),x],x]D(x){\in}rad(A)$ or $D(x)[[D(x),x],x]{\in}rad(A)$ for all $x{\in}A$. In this case, we show that $D(A){\subseteq}rad(A)$.

• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.443-455
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• 2008

For an extension $A\;{\subseteq}\;B$ of commutative rings, we present a sufficient conditio for the ring $[[A^{S,\;\leq}]]$ of generalized power series to be weakly normal (resp., stronglyt-closed) in $[[B^{S,\;\leq}]]$, where (S, $\leq$) be a torsion-free cancellative strictly ordered monoid. As a corollary, it can be applied to the ring of power series in infinitely many indeterminates as well as in finite indeterminates.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.995-1004
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• 2000

In this paper we shall give a slight generalization of J. Vukman's Theorem. And show from the result that the image of a continuous linear Jordan derivation on a noncommutative Banach algebra A is contained in the radical under the condition [D(x),x]E(x) ${\in}$ rad(A) for all $x{\in}A$ . And we show some properties of the derivations on noncommutative Banach algebras.

• 충청수학회지
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• 제31권1호
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• pp.1-12
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• 2018

Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation $D:R{\rightarrow}R$ such that $D^2(x)[D(x),x]=0$ or $[D(x),x]D^2(x)=0$ for all $x{\in}R$. In this case we have $f(x)^5=0$ for all $x{\in}R$. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A{\rightarrow}A$ such that $D^2(x)[D(x),x]{\in}rad(A)$ or $[D(x),x]D^2(x){\in}rad(A)$ for all $x{\in}A$. In this case, we show that $D(A){\subseteq}rad(A)$.