• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.83-94
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• 2016

Let M and N be modules over a ring R. The purpose of this paper is to study modules M, N for which the bi-module [M, N] is regular or pi. It is proved that the bi-module [M, N] is regular if and only if a module N is semi M-projective and $Im({\alpha}){\subseteq}^{\oplus}N$ for all ${\alpha}{\in}[M,N]$, if and only if a module M is semi N-injective and $Ker({\alpha}){\subseteq}^{\oplus}N$ for all ${\alpha}{\in}[M,N]$. Also, it is proved that the bi-module [M, N] is pi if and only if a module N is direct M-projective and for any ${\alpha}{\in}[M,N]$ there exists ${\beta}{\in}[M,N]$ such that $Im({\alpha}{\beta}){\subseteq}^{\oplus}N$, if and only if a module M is direct N-injective and for any ${\alpha}{\in}[M,N]$ there exists ${\beta}{\in}[M,N]$ such that $Ker({\beta}{\alpha}){\subseteq}^{\oplus}M$. The relationship between the Jacobson radical and the (co)singular ideal of [M, N] is described.

• 대한수학회보
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• 제38권4호
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• pp.689-699
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• 2001

We discuss the class of projective systems whose supports are the complement of the union of three linear subspaces in general position. We proves these codes are uniquely dtermined up to equivalence by their weight enumerators. Our result is a generalization of the result given in [1].

• 대한수학회보
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• 제38권4호
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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.

• 대한수학회보
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• 제41권1호
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• pp.19-25
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• 2004

In our previous paper (Bull. Korean Math. Soc. 37(2000), 493-505), we claimed a theorem on a certain subset of a projective space over a finite field (Theorem 3.1). Recently, however, Professor Kato pointed out that our proof does not work if the field consists of two elements. Here we give an alternative proof of the theorem for the exceptional case.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.243-257
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• 1998

The purpose of this paper is to give some characterizations of $n$-dimensional CR-submanifolds with ($n-1$) CR-dimension immersed in a complex projective space $CP^{\frac{n+2}{2}}$, in terms of the Riemannian curvature tensor R.

• 호남수학학술지
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• 제28권4호
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• pp.499-511
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• 2006

It is well-known that every finitely generated torsion-free module over a principal ideal domain is free. This will be generalized. We deal with ideals of the finite, external direct product of certain rings. Finally, if M is a torsion-free, finitely generated module over a reduced, Noetherian ring A, then we prove that Ms is a projective module over As, where $S=A{\setminus}(A)$.

• 호남수학학술지
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• 제39권4호
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• pp.677-688
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• 2017

Let P be a finitely generated projective module over a commutative ring R with identity. If P has finite rank, then it will be shown that the map ${\varphi}:Aut_R(P){\rightarrow}U(R)$ defined by ${\varphi}({\alpha})={\det}({\alpha})$ is locally surjective and $Ker({\varphi})=SL_R(P)$.

• 대한수학회논문집
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• 제17권4호
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• pp.625-633
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• 2002

Recently, Chen establishes sharp relationship between the k-Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. In this paper, we establish sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in quaternion projective spaces.

• Korean Journal of Mathematics
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• 제22권3호
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• pp.501-516
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• 2014

We define the class of almost ${\omega}_1-p^{\omega+n}$-projective abelian p-primary groups and investigate their basic properties. The established results extend classical achievements due to Hill (Comment. Math. Univ. Carol., 1995), Hill-Ullery (Czech. Math. J., 1996) and Keef (J. Alg. Numb. Th. Acad., 2010).

• 대한수학회보
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• 제39권2호
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• pp.327-332
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• 2002

In this paper we prove that if M is a J-invariant sub-manifold of codimension 2 in a complex projective space $P_{n+1}(C)$, and the second fundamental tensor is cyclic-parallel or M has harmonic curvature, then M is locally complex quadric Q$_n$(C) or P$_n$(C).