• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.453-467
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• 2005

Let K be an algebraic number field. If k is the maximal cyclotomic subextension in K then the Schur K-group S(K) is obtained from the Schur k-group S(k) by scalar extension. In the paper we study projective Schur group PS(K) which is a generalization of Schur group, and prove that a projective Schur K-algebra is obtained by scalar extension of a projective Schur k-algebra where k is the maximal radical extension in K with mild condition.

• 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.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.1-11
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• 2002

A Schur algebra was generalized to projective Schur algebra by admitting twisted group algebra. A Schur algebra is a projective Schur algebra with trivial 2-cocycle. In this paper we study situations that Schur algebra is a projective Schur algebra with nontrivial cocycle, and we find a criterion for a projective Schur algebra to be a Schur algebra.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1689-1696
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• 2014

Recently, it was proved that every p-Schur ring over an abelian group of order $p^3$ is Schurian. In this paper, we prove that every commutative p-Schur ring over a non-abelian group of order $p^3$ is Schurian.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.125-140
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• 2006

In 1933, I. Schur introduced a Schur ring in connection with permutation group and regular subgroup. After then, it was studied mostly for purely group theoretical purposes. In 1970s, Klin and Poschel initiated its usage in the investigation of graphs, especially for Cayley and circulant graphs. Nowadays it is known that Schur ring is one of the best way to enumerate Cayley graphs. In this paper we study the origin of Schur ring back to 1933 and keep trace its evolution to graph theory and combinatorics.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.803-814
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• 2001

A projective Schur algebra associated with a partition of finite group G can be constructed explicitly by defining linear transformations of G. We will consider various linear transformations and count the number of equivalent classes in a finite group. Then we construct projective Schur algebra dimension is determined by the number of classes.

• 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.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.77-85
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• 2001

If an Azumaya algebra A is a homomorphic image of a finite group ring RG where G is a direct product of subgroups then A can be decomposed into subalgebras A(sub)i which are homomorphic images of subgroup rings of RG. This result is extended to projective Schur algebras, and in this case behaviors of 2-cocycles will play major role. Moreover considering the situation that A is represented by Azumaya group ring RG, we study relationships between the representing groups for A and A(sub)i.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.303-306
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• 2004

There are 49 non-metacyclic p-groups of order less than 1000 with trivial Schur multiplier. In this paper we give a list of deficiency zero presentations for these groups.

• 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.