• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.733-744
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• 2020

Let 𝕽 be a commutative ring with unity, A and B be 𝕽-algebras, M be a (A, B)-bimodule and N be a (B, A)-bimodule. The 𝕽-algebra 𝕾 = 𝕾(A, M, N, B) is a generalized matrix algebra defined by the Morita context (A, B, M, N, 𝝃_MN, Ω_NM). In this article, we study generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.133-139
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• 2022

We offered a new method for constructing Latin squares. We introduce the concept of a standard form via example for Latin squares of order n and we also call it symmetric BCL algebras matrix, and thereby become BCL algebra representations of the picture of Latin squares. Our research shows that some new properties of the Latin squares with BCL algebras are in ℤ_n.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.641-648
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• 2003

In this paper, we characterize the compact sets full-invariant properties, dual invariant properties and quasi full invariant properties in a class of infinite matrix algebras.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.41-50
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• 2018

This paper mainly considers a tuple of multiplication operators on Bergman spaces over polydisks which essentially arise from a matrix, their joint reducing subspaces and associated von Neumann algebras. It is shown that there is an interesting link of the non-triviality for such von Neumann algebras with the determinant of the matrix. A complete characterization of their abelian property is given under a more general setting.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.997-1000
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• 2010

We prove that the reduced free product of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras is not the minimal tensor product of reduced free products of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras. It is shown that the reduced group $C^*$-algebra associated with a group having the property T of Kazhdan is not isomorphic to a reduced free product of abelian $C^*$-algebras or the minimal tensor product of such reduced free products. The infinite tensor product of reduced free products of abelian $C^*$-algebras is not isomorphic to the tensor product of a nuclear $C^*$-algebra and a reduced free product of abelian $C^*$-algebra. We discuss the freeness of free product $II_1$-factors and solidity of free product $II_1$-factors weaker than that of Ozawa. We show that the freeness in a free product is related to the existence of Cartan subalgebras in free product $II_1$-factors. Finally, we give a free product factor which is not solid in the weak sense.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2027-2034
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• 2013

In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from $M_n(\mathcal{A})$ ($\mathcal{A}$ is not necessarily a prime algebra) onto an arbitrary ring $\mathcal{R}^{\prime}$ is additive.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.169-178
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• 2007

We consider the set of $n{\times}n$ idempotent matrices and we characterize the linear operators that preserve idempotent matrices over Boolean algebras. We also obtain characterizations of linear operators that preserve idempotent matrices over a chain semiring, the nonnegative integers and the nonnegative reals.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.669-677
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• 1996

Let $M_n$ be the $C^*$-algebra of all $n \times n$ matrices over the complex field, and $P[M_m, M_n]$ the convex cone of all positive linear maps from $M_m$ into $M_n$ that is, the maps which send the set of positive semidefinite matrices in $M_m$ into the set of positive semi-definite matrices in $M_n$. The convex structures of $P[M_m, M_n]$ are highly complicated even in low dimensions, and several authors [CL, KK, LW, O, R, S, W]have considered the possibility of decomposition of $P[M_m, M_n] into subcones.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.247-259
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• 2016

We first give the constructions of (Jordan) higher derivations on a trivial extension algebra and then we provide some sufficient conditions under which a Jordan higher derivation on a trivial extension algebra is a higher derivation. We then proceed to the trivial generalized matrix algebras as a special trivial extension algebra. As an application we characterize the construction of Jordan higher derivations on a triangular algebra. We also provide some illuminating examples of Jordan higher derivations on certain trivial extension algebras which are not higher derivations.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.419-433
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• 2012

In this paper, we show that under certain conditions every Lie higher derivation and Lie triple derivation on a triangular algebra are proper, respectively. The main results are then applied to (block) upper triangular matrix algebras and nest algebras.