• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.397-408
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• 2016

Let R be a 2-torsion free prime ring with center Z, U be the Utumi quotient ring, Q be the Martindale quotient ring of R, d be a derivation of R and L be a Lie ideal of R. If $d(uv)^n=d(u)^md(v)^l$ or $d(uv)^n=d(v)^ld(u)^m$ for all $u,v{\in}L$, where m, n, l are xed positive integers, then $L{\subseteq}Z$. We also examine the case when R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on non-commutative Banach algebras. This result simultaneously generalizes a number of results in the literature.

• 대한수학회논문집
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• 제32권4호
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• pp.789-803
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• 2017

Let $K={\mathbb{Q}}({\alpha})$ be a cubic field where ${\alpha}$ is an algebraic integer such that $disc_K({\alpha})$ is square-free. In this paper we will classify the structure of the unit group of the quotient ring ${\mathcal{O}}_K/A$ for each non-zero ideal A of ${\mathcal{O}}_K$.

• 대한수학회논문집
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• 제9권4호
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• pp.797-801
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• 1994

In [3] Goldman introduced the notion of modules of quotients of a ring with respect to an idempotents kernel functor, which is a generalization of the localization of a module with respect to a multiplicative subset of a communtative ring. For an idempotent kernel functor $\sigma$ on the category of R-modules and for an R-module M, let $Q_\sigma(M)$ denote the module of quotients with respect to $\sigma$.

• 대한수학회보
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• 제55권3호
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• pp.921-935
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• 2018

In this study we determine the structure of m-adic residue codes over the non-chain ring $F_q[v]/(v^2-v)$ and present some promising examples of such codes that have optimal parameters with respect to Griesmer Bound. Further, we show that the generators of m-adic residue codes serve as a natural and suitable application for generating reversible DNA codes via a special automorphism and sets over $F_{4^{2k}}[v]/(v^2-v)$.

• Kyungpook Mathematical Journal
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• 제50권1호
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• pp.1-5
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• 2010

Let P be a prime ideal of a commutative unital ring R; X an indeterminate; D := R/P; L the quotient field of D; F an algebraic closure of L; ${\alpha}$ ${\in}$ L[X] a monic irreducible polynomial; ${\xi}$ any root of in F; and Q = ${\alpha}$>, the upper to P with respect to ${\alpha}$. Then R[X]/Q is R-algebra isomorphic to $D[{\xi}]$; and is R-isomorphic to an overring of D if and only if deg(${\alpha}$) = 1.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.397-406
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• 2023

Let R be a commutative ring with identity, X be an indeterminate over R, and R[X] be the polynomial ring over R. In this paper, we study when R[X] is a radically principal ideal ring. We also study the t-operation analog of a radically principal ideal domain, which is said to be t-compactly packed. Among them, we show that if R is an integrally closed domain, then R[X] is t-compactly packed if and only if R is t-compactly packed and every prime ideal Q of R[X] with Q ∩ R = (0) is radically principal.

• East Asian mathematical journal
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• 제38권1호
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• pp.1-12
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• 2022

Let R be a ring with an endomorphism σ and a σ-derivation δ. R is called (σ, δ)-Baer (resp. (σ, δ)-quasi-Baer, (σ, δ)-p.q.-Baer, (σ, δ)-p.p.) if the right annihilator of every right (σ, δ)-set (resp., (σ, δ)-ideal, principal (σ, δ)-ideal, (σ, δ)-element) of R is generated by an idempotent of R. In this paper, for a given Ore extension A = R[x; σ, δ] of R, the following properties are investigated: If R is a σ-rigid ring in which σ and δ commute, then (1) R is (σ, δ)-Baer if and only if R is (σ, δ)-quasi-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-quasi-Baer; (2) R is (σ, δ)-p.p. if and only if R is (σ, δ)-p.q.-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.p. if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.q.-Baer.

• 대한수학회보
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• 제55권1호
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• pp.187-204
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• 2018

Let $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}\;R_{\alpha}$ be a graded integral domain, H be the set of nonzero homogeneous elements of R, and ${\star}$ be a semistar operation on R. The purpose of this paper is to study the properties of $quasi-Pr{\ddot{u}}fer$ and UMt-domains of graded integral domains. For this reason we study the graded analogue of ${\star}-quasi-Pr{\ddot{u}}fer$ domains called $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. We study several ring-theoretic properties of $gr-{\star}-quasi-Pr{\ddot{u}}fer$ domains. As an application we give new characterizations of UMt-domains. In particular it is shown that R is a $gr-t-quasi-Pr{\ddot{u}}fer$ domain if and only if R is a UMt-domain if and only if RP is a $quasi-Pr{\ddot{u}}fer$ domain for each homogeneous maximal t-ideal P of R. We also show that R is a UMt-domain if and only if H is a t-splitting set in R[X] if and only if each prime t-ideal Q in R[X] such that $Q{\cap}H ={\emptyset}$ is a maximal t-ideal.

• Bulletin of the Korean Chemical Society
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• 제25권5호
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• pp.704-710
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• 2004

A poly(1-hexyl-3,4-dimethyl-2,5-pyrrolylene) (PHDP) was prepared and its luminescence in tetrahydrofuran (THF) was studied. When PHDP is excited by UV light, it produces very strong blue luminescence. The quantum yield of PHDP (Q = 36.9%) is much greater than that of the monomer, 1-hexyl-3,4-dimethylpyrrole (HDP) with Q = 0.61%. The principal luminescence of PHDP has a single decay component with ca. 1 ns, whereas the decay of HDP is complicated. The molecular structure and conformational behavior of HDP and the oligomers up to trimer have been also determined by ab initio Hartree-Fock (HF/6-31$G^{**}$), density functional theory (DFT-B3LYP/6-31$G^{**}$), and semiempirical (ZINDO) methods. According to the results of calculations, it is proposed that the enhanced quantum yield of the polymer PHDP results mostly from the ${\pi}$-conjugation between neighboring pyrrole rings.

• 한국균학회지
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• 제51권2호
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• pp.101-109
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• 2023

A fungal strain designated KNUF-21-66Q1 was isolated from soil in Chungcheongbuk Province, Korea. Moderate growth of colonies was observed on potato dextrose agar, oatmeal agar (OA), malt extract agar, and cornmeal agar media at 25℃, and the detailed morphology was examined on OA medium. The colonies on OA medium were flat, had entire margin, hyaline, and yellow concentric rings in 3-4 weeks. Conidiomata were pycnidial, solitary or clustered, globose to subglobose, black-brown, and 300-500 ㎛ in diameter. Conidiogenous cells were smooth, hyaline, globose to ampulliform, and 6.0-9.0×3.0-6.0 ㎛ in size (n=15). Conidia were hyaline to pale brown, slightly golden, obovoid to slightly ellipsoidal, smooth, guttulate, and 3.0-4.7×2.1-3.3 ㎛ in size (n=100). The strain was confirmed based on phylogenetic analysis using internal transcribed spacer regions, the partial 28S rDNA of large subunit, and β-tubulin gene sequences. The morphological observations and phylogenetic analysis revealed that the strain KNUF-21-66Q1 was similar to the previously described Paraconiothyrium kelleni. To our knowledge, this is the first report of P. kelleni in Korea.