• 대한수학회보
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• 제37권3호
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• pp.429-435
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• 2000

Our main goal is to show that if there exist Jordan derivations D, E and G on a noncommutative 2-torsion free prime ring R such that$(G^2(x)+E(x))D(x)=0\ or\ D(x)(G^2(x)+E(x))=0\ for\ all\ x\inR$, then we have D=o or E=0, G=0.

• 대한수학회지
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• 제34권2호
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• pp.453-467
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• 1997

A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권4호
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• pp.347-375
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• 2016

Let R be a 3!-torsion free noncommutative semiprime ring, U a Lie ideal of R, and let $D:R{\rightarrow}R$ be a Jordan derivation. If [D(x), x]D(x) = 0 for all $x{\in}U$, then D(x)[D(x), x]y - yD(x)[D(x), x] = 0 for all $x,y{\in}U$. And also, if D(x)[D(x), x] = 0 for all $x{\in}U$, then [D(x), x]D(x)y - y[D(x), x]D(x) = 0 for all $x,y{\in}U$. And we shall give their applications in Banach algebras.

• 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.

• 대한수학회보
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• 제47권1호
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• pp.151-157
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• 2010

In this note, we obtain range inclusion results for left Jordan derivations on Banach algebras: (i) Let $\delta$ be a spectrally bounded left Jordan derivation on a Banach algebra A. Then $\delta$ maps A into its Jacobson radical. (ii) Let $\delta$ be a left Jordan derivation on a unital Banach algebra A with the condition sup{r$(c^{-1}\delta(c))$ : c $\in$ A invertible} < $\infty$. Then $\delta$ maps A into its Jacobson radical. Moreover, we give an exact answer to the conjecture raised by Ashraf and Ali in [2, p. 260]: every generalized left Jordan derivation on 2-torsion free semiprime rings is a generalized left derivation.

• 한국논리학회:학술대회논문집
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• 한국논리학회 2009년도 동계학술 발표회
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• pp.38-66
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• 2009

Weakening-free non-associative fuzzy logics, which are based on mica-norms, are introduced as non-associative substructural logics extending $GL_{e\bot}$ (Non-associative Full Lambek calculus with exchange and constants T, F) introduced by Galatos and Ono (cf. see [10, 11]). First, the mica-norm logic MICAL, which is intended to cope with the tautologies of left-continuous conjunctive mica-norms and their residua, and several axiomatic extensions of it are introduced as weakening-free non-associative fuzzy logics. The algebraic structures corresponding to the systems are then defined, and algebraic completeness results for them are provided. Next, standard completeness (i,e. completeness with respect to algebras whose lattice reduct is the real unit interval [0, 1]) is established for these logics by using Jenei and Montagna-style approach for proving standard completeness in [7, 18].

• 한국수학사학회지
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• 제17권2호
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• pp.97-103
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• 2004

이 논문에서는 다원환의 자유결합의 대수적 구조를 규명하여 분수확대체로서의 미분가군의 일반적인 특성을 연구하고 있다. 보편적 범주 내에서의 미분과 미분가군의 대수적 형태는 대수적 결합의 기본 원칙을 충실히 보존한다는 원칙을 밝혔을 뿐만 아니라 대수적 동형 개념으로 수학의 우주적 균형이론을 실질적으로 보여주고 있다.

• 대한수학회지
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• 제49권2호
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• pp.405-417
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• 2012

We find the Hilbert function and the minimal free resolution of a star-configuration in $\mathbb{P}^n$. The conditions are provided under which the Hilbert function of a star-configuration in $\mathbb{P}^2$ is generic or non-generic We also prove that if $\mathbb{X}$ and $\mathbb{Y}$ are linear star-configurations in $\mathbb{P}^2$ of types t and s, respectively, with $s{\geq}t{\geq}3$, then the Artinian k-algebra $R/(I_{\mathbb{X}}+I_{\mathbb{Y})$ has the weak Lefschetz property.

• 대한수학회논문집
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• 제20권4호
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• pp.751-763
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• 2005

For a given gauge invariant state $\omega$ on the CAR algebra A isomorphic with the C$\ast$ -algebra of $2{\times}2$ complex matrices, we construct a family of quantum Markov semigroups on A which leave w invariant. By analyzing their generators, we decompose the algebra A into four eigenspaces of the semigroups and show some properties.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권3호
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• pp.261-268
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• 2011

For a compact Hausdorff space X with its p-fold covering map ${\sigma}$, we construct its corresponding topological groupoid ${\Gamma}$, and show that there is a strong relation between the dynamical structures of (X, ${\sigma}$) and the groupoid structures of ${\Gamma}$.