• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.35-49
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• 2005

For an extension field K of k, a restriction homomorphism on Brauer k-group B(k) maps Brauer k-algebras to Brauer K- algebras by tensor product. A purpose of this work is to study the restriction map that sends radical (Schur) k-algebras to radical (Schur) K-algebras. And we ask an analogous question with respect to corestriction map on Brauer group B(K) that whether the corestriction map sends radical K-algebras to radical k-algebras.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.135-137
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• 1989

Let R be a Krull domain with field of fractions K. By Br(R) we denote the Brauer group of R. Studying the Kernel of the homomorphism Br(R).rarw.Br(K), Orzech defined Brauer groups Br(M) for different categories M of R-modules [4]. In this paper we show that an algebra A in Br(D) is a maximal order in A K and that the map Br(D).rarw. Br(K) is one to one. We note here few conventions. All rings are Krull domains and all modules will be unitary. By Z we donote the set of height one prime ideals of a Krull domain.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.1-28
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• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• Journal of the Korean Mathematical Society
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• v.17 no.2
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• pp.265-267
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• 1981

• Communications of the Korean Mathematical Society
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• v.4 no.1
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• pp.89-93
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• 1989

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.527-539
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• 1995

We consider the Schur groups of some module categories, which are subcategories of category of divisorial modules over a Krull domain. Then we obtain the exact sequence connecting class group, Schur class group and Schur groups of these categories.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.527-532
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• 1998

We study some properties of Schur functor and its sub-functions related to separable algebras and cyclotomic algebras.