• 대한수학회논문집
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• 제32권3호
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• pp.495-502
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• 2017

Let R be a 2-torsion free prime ring and J be a nonzero Jordan ideal of R. Let F and G be two generalized derivations with associated derivations f and g, respectively. Our main result in this paper shows that if F(x)x - xG(x) = 0 for all $x{\in}J$, then R is commutative and F = G or G is a left multiplier and F = G + f. This result with its consequences generalize some recent results due to El-Soufi and Aboubakr in which they assumed that the Jordan ideal J is also a subring of R.

• 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.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.709-717
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• 2022

The objective of this research is to prove that an additive mapping T : R → R is a left as well as right centralizer on R if it satisfies any one of the following identities: (i) T(xⁿyⁿ + yⁿxⁿ) = T(xⁿ)yⁿ + yⁿT(xⁿ) (ii) 2T(xⁿyⁿ) = T(xⁿ)yⁿ + yⁿT(xⁿ) for each x, y ∈ R, where n ≥ 1 is a fixed integer and R is any n!-torsion free semiprime ring. In addition, we talk over above identities in the setting of *-ring(ring with involution).

• 대한수학회보
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• 제54권2호
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• pp.559-571
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• 2017

We investigate modules M having the injective property relative to nonsingular modules. Such modules are called "$\mathcal{N}$-injective modules". It is shown that M is an $\mathcal{N}$-injective R-module if and only if the annihilator of $Z_2(R_R)$ in M is equal to the annihilator of $Z_2(R_R)$ in E(M). Every $\mathcal{N}$-injective R-module is injective precisely when R is a right nonsingular ring. We prove that the endomorphism ring of an $\mathcal{N}$-injective module has a von Neumann regular factor ring. Every (finitely generated, cyclic, free) R-module is $\mathcal{N}$-injective, if and only if $R^{(\mathbb{N})}$ is $\mathcal{N}$-injective, if and only if R is right t-semisimple. The $\mathcal{N}$-injective property is characterized for right extending rings, semilocal rings and rings of finite reduced rank. Using the $\mathcal{N}$-injective property, we determine the rings whose all nonsingular cyclic modules are injective.

• Bulletin of the Korean Chemical Society
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• 제12권2호
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• pp.143-148
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• 1991

In the unhydrated and hydrated states, conformational free energies of L-ascorbic acid anion (AAA) were computed with an empirical potential function and the hydration shell model (a program CONBIO). The conformational energy was minimized from possible starting conformations expressed with five torsion angles of the molecule. The conformational entropy of each low energy conformation in both states was computed using a harmonic approximation. As found in L-ascorbic acid (AA), intramolecular hydrogen bonds (HBs) are proved to be of significant importance in stabilizing the overall conformations of AAA in both states, and give the folded conformations, which are quite different from those in crystal. There are competitions between HBs and hydration around O3 atom of the lactone ring and hydroxyls of the acyclic side chain. Especially, the whole conformation of AAA is strongly dependent on the water-accessibility of O3 atom. Though there is a significant effect of the hydration on conformational surface, the lowest energy conformation of the unhydrated AAA is conserved. The different patterns of HBs and hydration result in the conformations of AAA in both states being different from those of AA. It can be drawn by several feasible conformations obtained in the hydrated state that there exists an ensemble of several conformations in aqueous solution.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.683-710
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• 2020

Let ℕ be the set of nonnegative integers and 𝕬 be a 2-torsion free triangular algebra over a commutative ring ℛ. In the present paper, under some lenient assumptions on 𝕬, it is proved that if Δ = {𝛿_n}_n∈ℕ is a sequence of ℛ-linear mappings 𝛿_n : 𝕬 → 𝕬 satisfying ${\delta}_n([[x,\;y],\;z])\;=\;\displaystyle\sum_{i+j+k=n}\;[[{\delta}_i(x),\;{\delta}_j(y)],\;{\delta}_k(z)]$ for all x, y, z ∈ 𝕬 with xy = 0 (resp. xy = p, where p is a nontrivial idempotent of 𝕬), then for each n ∈ ℕ, 𝛿_n = d_n + 𝜏_n; where d_n : 𝕬 → 𝕬 is ℛ-linear mapping satisfying $d_n(xy)\;=\;\displaystyle\sum_{i+j=n}\;d_i(x)d_j(y)$ for all x, y ∈ 𝕬, i.e. 𝒟 = {d_n}_n∈ℕ is a higher derivation on 𝕬 and 𝜏_n : 𝕬 → Z(𝕬) (where Z(𝕬) is the center of 𝕬) is an ℛ-linear map vanishing at every second commutator [[x, y], z] with xy = 0 (resp. xy = p).

• Journal of Chest Surgery
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• 제44권2호
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• pp.115-122
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• 2011

Background: The intramural coronary artery has been known as a risk factor for early death after an arterial switch operation (ASO). We reviewed the morphological characteristics and evaluated the early and mid-term results of ASO for patients with an intramural coronary artery. Materials and Methods: From March 1994 to September 15th 2010, 158 patients underwent ASO at Dong-A and Pusan National University Hospitals for repair of transposition of the great arteries and double outlet right ventricle. Among these patients, 14 patients (8.9%) had an intramural coronary artery. Mean age at operation was $13.4{\pm}10.2$ days (4 to 39 days) and mean body weight was $3.48{\pm}0.33$ kg (2.88 to 3.88 kg). All patients except one were male. Eight patients had TGA/IVS and 4 patients had an aortic arch anomaly. Two patients (14.3%) had side-by-side great artery relation, of whom one had an intramural right coronary artery and the other had an intramural left anterior descending coronary artery. Twelve patients had anterior-posterior relation, all of whom had an intramural left coronary artery (LCA). The aortocoronary flap technique was used in coronary transfer in 8 patients, of whom one patient required a switch to the individual coronary button technique 2 days after operation because of myocardial ischemia. An individual coronary button implantation technique was adopted in 6, of whom 2 patients required left subclavian artery free graft to LCA during the same operation due to LCA injury during coronary button mobilization and LCA torsion. Results: There was 1 operative death (7.1%), which occurred in the first patient in our series. This patient underwent an aortocoronary flap procedure for coronary transfer combining aortic arch repair. Overall operative mortality for 144 patients without an intramural coronary artery was 13.2% (19/144). There was no statistical difference in operative mortality between the patients with and without an intramural coronary artery (p>0.1). There was no late death. The mean follow-up duration was $52.1{\pm}43.0$ months (0.5 to 132 months). One patient who had a subclavian artery free graft required LCA stenting 6.5 years after surgery for LCA anastomotic site stenosis. No other surviving patient needed any intervention for coronary problems. All patients had normal ventricular function at latest echocardiography and were in NYHA class 1. Conclusion: The arterial switch operation in Transposition of Great Arteries or Double Outlet Right Ventricle patients with intramural coronary can be performed with low mortality; however, there is a high incidence of intraoperative or postoperative coronary problems, which can be managed with conversion to the individual coronary button technique and a bypass procedure using a left subclavian free graft. Both aortocoronary flap and individual coronary button implantation techniques for coronary transfer have excellent mid-term results.