• Communications of the Korean Mathematical Society
• /
• v.15 no.2
• /
• pp.331-338
• /
• 2000

In the present paper, we investigate a problem in a sym-metric Finsler space, which is a special space. First we prove that if a symmetric space remains to be a symmetric one under the Z-projective change, then the space is of zero curvature. Further we will study W-recurrent space and D-recurrent space under the pro-jective change.

• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.403-416
• /
• 2021

It is known that the rank 2 stably free syzygy module P⁽²⁾ is not free. This algebraic fact was proved analytically, but this remarkable fact still lacks of a simple algebraic proof. The main purpose of this paper is to give a partially algebraic proof by making use of a theorem whose proof is quite topological, and the further properties of the module will be discussed.

• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.1113-1129
• /
• 2019

We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.

• Journal of the Chungcheong Mathematical Society
• /
• v.34 no.3
• /
• pp.235-251
• /
• 2021

The aim of the present paper is to study 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection. Firstly, we prove that extended generalized M-projective 𝜙-recurrent 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection is an 𝜂-Einstein manifold with respect to Levi-Civita connection under some certain conditions. Later we study some curvature properties of 3-dimensional trans-Sasakian manifold admitting the above connection.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.5
• /
• pp.1289-1304
• /
• 2022

In this note, we show that a strongly 𝜙-ring R is a 𝜙-PvMR if and only if any 𝜙-torsion-free R-module is 𝜙-w-flat, if and only if any GV-torsion-free divisible R-module is nonnil-absolutely w-pure, if and only if any GV-torsion-free h-divisible R-module is nonnil-absolutely w-pure, if and only if any finitely generated nonnil ideal of R is w-projective.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.185-201
• /
• 2023

With the notion of prime submodule defined by F. Raggi et al. we prove that the intersection of all prime submodules of a Goldie module M is a nilpotent submodule provided that M is retractable and M^(Λ)-projective for every index set Λ. This extends the well known fact that in a left Goldie ring the prime radical is nilpotent.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.405-423
• /
• 2023

Let (𝓛, 𝒜) be a complete duality pair. We give some equivalent characterizations of Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures associated to duality pairs and Frobenius pairs. Some rings are described by Frobenius pairs. In addition, we investigate special Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures and recollements associated to them.

• Kyungpook Mathematical Journal
• /
• v.15 no.1
• /
• pp.51-54
• /
• 1975

• Kyungpook Mathematical Journal
• /
• v.21 no.1
• /
• pp.91-115
• /
• 1981

• Journal of the Korean Mathematical Society
• /
• v.10 no.1
• /
• pp.35-39
• /
• 1973