• 대한수학회보
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• 제59권3호
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• pp.781-787
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• 2022

In this paper, we show that under certain conditions the Wedderburn decomposition of a finite semisimple group algebra 𝔽_qG can be deduced from a subalgebra 𝔽_q(G/H) of factor group G/H of G, where H is a normal subgroup of G of prime order P. Here, we assume that q = p^r for some prime p and the center of each Wedderburn component of 𝔽_qG is the coefficient field 𝔽_q.

• 대한수학회보
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• 제58권4호
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• pp.865-876
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• 2021

Let 𝔽 be a commutative ring. A restricted skew polynomial extension over 𝔽 is a class of iterated skew polynomial 𝔽-algebras which include well-known quantized algebras such as the quantum algebra U_q(𝔰𝔩₂), Weyl algebra, etc. Here we obtain a necessary and sufficient condition in order to be restricted skew polynomial extensions over 𝔽. We also introduce a restricted Poisson polynomial extension which is a class of iterated Poisson polynomial algebras and observe that a restricted Poisson polynomial extension appears as semiclassical limits of restricted skew polynomial extensions. Moreover, we obtain usual as well as unusual quantized algebras of the same Poisson algebra as applications.

• 대한수학회논문집
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• 제35권2호
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• pp.487-497
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• 2020

In this paper, we establish a complex matrix representation of the Clifford algebra Cℓ_p,q. The size of our representation is significantly smaller than the size of the elements in L_p,q(ℝ). Additionally, we give detailed information about the spectrum of the constructed matrix representation.

• East Asian mathematical journal
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• 제18권2호
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• pp.205-209
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• 2002

In the paper the following propositions are proved. 1) If ($Q,{\cdot},e$) is a B-algebra, then there exists a group($Q,A,^{-1}$, 1) such that the following equalities hold e=1 and ${\cdot}=^{-1}A$, where $^{-1}A(x,y)=z{\Longleftrightarrow^{def}}A(z,y)=x$; and 2) If ($Q,A,^{-1}$, e) is a group, then ($Q,^{-1}A$, e) is a B-algebra.

• Kyungpook Mathematical Journal
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• 제45권2호
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• pp.281-292
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• 2005

In this paper a nonlinear alternative of Leray-Schauder type is proved in a Banach algebra involving three operators and it is further applied to a functional nonlinear integral equation of mixed type $$x(t)=k(t,x({\mu}(t)))+[f(t,x({\theta}(t)))]\(q(t)+{\int}_0{^{\sigma}^{(t)}}v(t,s)g(s,x({\eta}\(s)))ds\)$$ for proving the existence results in Banach algebras under generalized Lipschitz and $Carath{\acute{e}}odory$ conditions.

• 대한수학회지
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• 제48권5호
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• pp.953-967
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• 2011

We show that the characteristic function $1S_{\underline{\alpha}}$ of any Harder-Narasimhan strata $S{\underline{\alpha}}\;{\subset}\;Coh_X^{\alpha}$ belongs to the spherical Hall algebra $H_X^{sph}$ of a smooth projective curve X (defined over a finite field $\mathbb{F}_q$). We prove a similar result in the geometric setting: the intersection cohomology complex IC(${\underline{S}_{\underline{\alpha}}$) of any Harder-Narasimhan strata ${\underline{S}}{\underline{\alpha}}\;{\subset}\;{\underline{Coh}}_X^{\underline{\alpha}}$ belongs to the category $Q_X$ of spherical Eisenstein sheaves of X. We show by a simple example how a complete description of all spherical Eisenstein sheaves would necessarily involve the Brill-Noether stratas of ${\underline{Coh}}_X^{\underline{\alpha}}$.

• 호남수학학술지
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• 제32권3호
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• pp.515-523
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• 2010

In this paper, we introduced a special set, called T-part, in a Q-algebra X. We also show that the T-part of X is a subalgebra of X. By using T-part, we provide an equivalent condition that every ideal is a T-ideal.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.795-807
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• 2009

The concepts of fuzzy pseudo ideals (resp. fuzzy pseudo p-ideals, associative fuzzy pseudo ideals, fuzzy pseudo q-ideals and fuzzy pseudo a-ideals) in a pseudo BCI-algebra are introduced, and related properties are investigated. Conditions for a fuzzy pseudo ideal to be a fuzzy pseudo p-ideal (resp. fuzzy pseudo q-ideal) are provided. A characterization and properties of an associative fuzzy pseudo ideal are given.

• East Asian mathematical journal
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• 제5권2호
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• pp.177-189
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• 1989

• 대한수학회논문집
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• 제27권3호
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• pp.431-439
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• 2012

Characterizations of $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) are provided. The notion of $\mathcal{N}$-subalgebras of type ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) is introduced, and its characterizations are discussed. Conditions for an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) (resp. ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) to be an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}$) are considered.