• 대한수학회논문집
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• 제33권1호
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• pp.165-170
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• 2018

In this paper, we show that every unital n-Jordan homomorphism ${\varphi}$ from a Banach algebra ${\mathcal{A}}$ onto a semisimple commutative Banach algebra B is continuous.

• 대한수학회보
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• 제22권2호
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• pp.89-93
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• 1985

One of the most important problems in automatic continuity theory is to solve the question of continuity of an algebra homomorphism from a Banach algebra into a semisimple Banach algebra with dense range. Many results on this subject are obtained imposing some conditions on the domains or the ranges of homomorphisms. For most recent results and references in automatic continuity theory one may refer to [1], [4] and [5]. In this note we study some properties of homomorphisms from $C^{*}$-algebras into Banach algebras. It is shown that the range of an isomorphism from a $C^{*}$-algebra into a Banach algebra contains no non zero element of the radical of B. Using this result we show that the same holds for a continuous homomorphism, hence a Banach algebra which is the image of a $C^{*}$-algebra under a continuous homomorphism is necessarily semisimple. Thus if there is a homomorphism from a $C^{*}$-algebra onto a non-semisimple Banach algebra it must be discontinuous. Also it follows that every non zero homomorphism from a $C^{*}$-algebra into a radical algebra is discontinuous. Then we make a brief observation on the behavior of quasinilpotent element of noncommutative $C^{*}$-algebras in relation with continuous homomorphisms.momorphisms.

• 대한수학회논문집
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• 제13권2호
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• pp.225-232
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• 1998

Let H be a finite dimensional Hopf algebra over a field k, and A be an H-module algebra over k which the H-action on A is D-continuous. We show that $Q_{max}(A)$, the maximal ring or quotients of A, is an H-module algebra. This is used to prove that if H is a finite dimensional semisimple Hopf algebra and A is a semiprime right(left) Goldie algebra than $A#H$ is a semiprime right(left) Goldie algebra. Assume that Asi a semiprime H-module algebra Then $A^H$ is left Artinian if and only if A is left Artinian.

• Kyungpook Mathematical Journal
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• 제57권4호
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• pp.601-612
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• 2017

Let Q be the frame g-loop quiver, i.e. a generalized ADHM quiver obtained by replacing the two loops into g loops. The vector space M of representations of Q admits an involution ${\ast}$ if orthogonal and symplectic structures on the representation spaces are endowed. We prove equivalence between semisimplicity of representations of the ${\ast}-invariant$ subspace N of M and the orbit-closedness with respect to the natural adjoint action on N. We also explain this equivalence in terms of King's stability [8] and orthogonal decomposition of representations.

• 대한수학회보
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• 제51권6호
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• pp.1605-1614
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• 2014

In continuation to the investigation initiated by Ferraz, Goodaire and Milies in [4], we provide an explicit description for the Wedderburn decomposition of finite semisimple group algebras of the class of finite groups G, such that $$G/Z(G){\simeq_-}C_2{\times}C_2$$, where Z(G) denotes the center of G.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1447-1457
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• 2009

In this paper we define intuitionistic fuzzy interior ideals in ordered semigroups. We prove that in regular(resp. intra-regular and semisimple) ordered semigroups the concepts of intuitionistic fuzzy interior ideals and intuitionistic fuzzy ideals coincide. We prove that an ordered semi group is intuitionistic fuzzy simple if and only if every intutionistic fuzzy interior ideal is a constant function. We characterize intra-regular ordered semi groups in terms of interior (resp. intuitionistic fuzzy interior) ideals.

• 대한수학회논문집
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• 제32권4호
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• pp.999-1008
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• 2017

By mainly using certain properties arising from the semisimple Lie group SO(2, 1), we aim to show how a family of some interesting formulas for bilateral series and integrals involving Whittaker, Bessel functions, and their product can be obtained.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.119-125
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• 2007

In this paper, we investigate the following: Let A be a semisimple Banach algebra. Suppose that there exists a linear derivation $f:A{\rightarrow}A$ such that the functional equation $<f(x),x>^2=0$ holds for all $x{\in}A$. Then we have $f=0$ on A.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.31-47
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• 2024

The concept of hybrid structures integrates two powerful mathematical tools: soft sets and fuzzy sets. This paper extends the application of hybrid structures to ordered hypersemigroups. We introduce the notions of hybrid interior hyperideals in ordered hypersemigroups and demonstrate their equivalence with hybrid hyperideals in certain classes, including regular, intra-regular, and semisimple ordered hypersemigroups. Furthermore, we provide a characterization of semisimple ordered hypersemigroups in terms of hybrid interior hyperideals.

• 대한수학회지
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• 제24권2호
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• pp.143-150
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• 1987