• 대한수학회보
• /
• 제55권1호
• /
• pp.25-40
• /
• 2018

We focus on the structure of the set of noncentral idempotents whose role is similar to one of central idempotents. We introduce the concept of quasi-Abelian rings which unit-regular rings satisfy. We first observe that the class of quasi-Abelian rings is seated between Abelian and direct finiteness. It is proved that a regular ring is directly finite if and only if it is quasi-Abelian. It is also shown that quasi-Abelian property is not left-right symmetric, but left-right symmetric when a given ring has an involution. Quasi-Abelian property is shown to do not pass to polynomial rings, comparing with Abelian property passing to polynomial rings.

• 대한수학회보
• /
• 제53권5호
• /
• pp.1395-1399
• /
• 2016

We will classify the finite barely non-abelian p-groups.

• 대한수학회보
• /
• 제52권4호
• /
• pp.1097-1105
• /
• 2015

The concept of tensor analogues of right 2-Engel elements in groups were defined and studied by Biddle and Kappe [1] and Moravec [9]. Using the automorphisms of a given group G, we introduce the notion of tensor analogue of 2-auto Engel elements in G and investigate their properties. Also the concept of $2_{\otimes}$-auto Engel groups is introduced and we prove that if G is a $2_{\otimes}$-auto Engel group, then $G{\otimes}$ Aut(G) is abelian. Finally, we construct a non-abelian 2-auto-Engel group G so that its non-abelian tensor product by Aut(G) is abelian.

• 정보보호학회논문지
• /
• 제25권3호
• /
• pp.567-571
• /
• 2015

Brezing과 Weng은 페어링 친화 타원곡선의 CM 파라미터들을 수체(number field)의 다항식 표현을 이용하여 생성하는 방법을 제안하였고, Freeman은 그 방법을 아벨 다양체(abelian variety)의 경우로 일반화 시켰다. 본 논문에서는 특히 단순 아벨 곡면(simple abelian surface)의 경우에 대해 Brezing-Weng 방법에서 사용되는 다항식족(polynomial family)을 구하는 새로운 공식들을 유도하고, 이를 이용하여 CM 파라미터들을 생성할 수 있음을 보인다.

• 대한수학회보
• /
• 제48권6호
• /
• pp.1219-1224
• /
• 2011

In this paper we give a determinant formula for congruent zeta functions of real Abelian function fields. We also give some example of congruent zeta functions when the conductor of real Abelian function field is monic irreducible.

• 대한수학회지
• /
• 제46권2호
• /
• pp.237-248
• /
• 2009

We give an explicit formula for the Mordell-Weil rank of an abelian fibered variety and some of its applications for an abelian fibered $hyperk{\ddot{a}}hler$ manifold. As a byproduct, we also give an explicit example of an abelian fibered variety in which the Picard number of the generic fiber in the sense of scheme is different from the Picard number of generic closed fibers.

• 대한수학회보
• /
• 제48권1호
• /
• pp.79-83
• /
• 2011

In the present paper we introduce the lower autocentral series of autocommutator subgroups of a given group. Following our previous work on the subject in 2009, it is shown that every finite abelian group is isomorphic with $n^{th}$-term of the lower autocentral series of some finite abelian group.

• Kyungpook Mathematical Journal
• /
• 제63권4호
• /
• pp.709-718
• /
• 2023

The inner automorphism groups of quandles are related to the classification problem of quandles. The inner automorphism group of a quandle is generated by inner automorphisms which are presented by columns in the operation table of the quandle. In this paper, we describe inner automorphisms of an abelian extension of a quandle by expressing columns of the operation table of the extended quandle as columns of the operation table of the original quandle. Such a description will be helpful in studying inner automorphism groups of abelian extensions of quandles.

• 대한수학회지
• /
• 제54권4호
• /
• pp.1109-1120
• /
• 2017

For an odd prime p, finite p-groups whose non-abelian subgroups have the same center are classified in this paper.

• 대한수학회보
• /
• 제51권6호
• /
• pp.1689-1696
• /
• 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.