• Korean Journal of Mathematics
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• v.21 no.1
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• pp.23-28
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• 2013

The structures of finite local rings of order ${\leq}$ 16 with nonzero Jacobson radical are investigated. The whole shape of non-commutative local rings of minimal order is completely determined up to isomorphism.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.445-454
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• 2011

In this paper, we extend some well known results concerning generalized derivations of prime rings to a generalized (${\sigma}$, ${\tau}$)-derivation.

• East Asian mathematical journal
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• v.26 no.3
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• pp.397-401
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• 2010

We investigate some properties of strongly reduced near-rings and left regular near-rings, also show that a strongly reduced near-ring is reduced. Next, we will characterize that reducibility, strong reducibility and left regularity in near-rings.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1049-1053
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• 2018

It is shown that any equidimensional local ring which has finite Cousin cohomology modules with respect to the dimension filtration has a uniform local cohomological annihilator and is universally catenary.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.529-540
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• 2009

The authors have investigated several properties of endomorphism rings of modules. In particular, a closedly simple module and a closedly semi-simple module were defined and then the regularities of its rings of endomorphisms were discussed.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1163-1173
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• 2021

In this paper, we obtain the MacWilliams identity for linear codes over finite chain rings with respect to homogeneous weight, and the product of chain rings.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.97-112
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• 2023

In this paper, we introduce and study the u-S-weak global dimension u-S-w.gl.dim(R) of a commutative ring R for some multiplicative subset S of R. Moreover, the u-S-weak global dimensions of factor rings and polynomial rings are investigated.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.237-243
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• 2010

In this paper, we investigate some properties of T-fuzzy subhypernear-rings of a hypernear-ring.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.959-972
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• 2013

Rege-Chhawchharia, and Nielsen introduced the concept of right McCoy ring, based on the McCoy's theorem in 1942 for the annihilators in polynomial rings over commutative rings. In the present note we concentrate on a natural generalization of a right McCoy ring that is called a right nilpotent coefficient McCoy ring (simply, a right NC-McCoy ring). The structure and several kinds of extensions of right NC-McCoy rings are investigated, and the structure of minimal right NC-McCoy rings is also examined.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.307-318
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• 2020

This article concerns the class of rings which satisfy the property of inserting regular elements at zero products, and rings with such property are called regular-IFP. We study the structure of regular-IFP rings in relation to various ring properties that play roles in noncommutative ring theory. We investigate conditions under which the regular-IFPness pass to polynomial rings, and equivalent conditions to the regular-IFPness.