• East Asian mathematical journal
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• v.36 no.1
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• pp.73-79
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• 2020

A ring R is called generalized regular if for every nonzero x in R there exists y in R such that xy is a nonzero idempotent. In this paper, we observe some equivalent conditions for the generalized regular rings that are abelian in terms of idempotents, and we also investigate the primitivity of an idempotent for such a ring. By using the investigation, we characterize such a kind of rings that are noetherian by showing that an abelian generalized regular ring R is noetherian if and only if R is isomorphic to a direct product of finitely many division rings. We also observe some interesting consequences of our results.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.10a
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• pp.139-142
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• 2004

The fabric composite rings for nozzle parts of solid rocket motors should be thick to endure high temperature and pressure of combustion gas. Since the thermal residual stresses developed during manufacturing of the axi-symmetric composite structures increase as the thickness increases and eventually induce failures during storage and operation, the estimation of the residual stresses is indispensable for design and manufacture of the thick composite nozzle parts. In this paper, thick fabric rings made of carbon fabric phenolic composites were fabricated in a hydroclave and in an autoclave using a multi-step pre-compaction process to minimize draping. The residual stresses distributed in the rings were measured by the radial-cut method and it was found that the compaction reduces the residual stresses in the composite ring.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.8
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• pp.878-883
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• 2008

In this paper, we propose a double rings structure to improve the balanced-port characteristics of Balun-Bandpass Filter(Balun-BPF). The conventional Balun-BPF has limitations on output symmetry and skirt steepness. We introduce a double rings structure and the suitable coupling point between the two ring resonators to solve these problems. The fabricated double rings Balun-BPF shows excellent characteristics as a Balun-BPF without the conventional limitations.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.723-735
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• 2006

In [2] it was shown that a 1-generator quasi-cyclic code C of length n = ml of index l over $\mathbb{Z}_4$ is free if C is generated by a polynomial which divides $X^m-1$. In this paper, we prove that a necessary and sufficient condition for a cyclic code over $\mathbb{Z}_pk$ of length m to be free is that it is generated by a polynomial which divides $X^m-1$. We also show that this can be extended to finite local rings with a principal maximal ideal.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.115-127
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• 2011

We study the structure of the set of nilpotent elements in various kinds of ring and introduce the concept of NR ring as a generalization of Armendariz rings and NI rings. We determine the precise relationships between NR rings and related ring-theoretic conditions. The Kothe's conjecture is true for the class of NR rings. We examined whether several kinds of extensions preserve the NR condition. The classical right quotient ring of an NR ring is also studied under some conditions on the subset of nilpotent elements.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1309-1325
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• 2016

This note focuses on a ring property in which upper and lower nilradicals coincide, as a generalizations of symmetric rings. The concept of symmetric ideal and ring in the noncommutative ring theory was initially introduced by Lambek, as an extension of the usual commutative ideal theory. The investigation of symmetric rings provided many useful results to the study in the noncommutative ring theory. So the results obtained from this study may be applicable to observing the structure of zero divisors in various kinds of algebraic systems containing matrix rings and polynomial rings.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.177-185
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• 2011

A right ideal I of a ring R is small in case for every proper right ideal K of R, K + I ${\neq}$ = R. A right R-module M is called PS-injective if every R-homomorphism f : aR ${\rightarrow}$ M for every principally small right ideal aR can be extended to R ${\rightarrow}$ M. A ring R is called right PS-injective if R is PS-injective as a right R-module. We develop, in this article, PS-injectivity as a generalization of P-injectivity and small injectivity. Many characterizations of right PS-injective rings are studied. In light of these facts, we get several new properties of a right GPF ring and a semiprimitive ring in terms of right PS-injectivity. Related examples are given as well.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.515-527
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• 2009

Let R be a commutative ring with identity. Then we prove $M_n(R)=GL_n(R)$ ${\cup}${$A{\in}M_n(R)\;{\mid}\;detA{\neq}0$ and det $A{\neq}U(R)$}${\cup}Z(M-n(R))$ where U(R) denotes the set of all units of R. In particular, it will be proved that the full matrix ring $M_n(F)$ over a field F is the disjoint union of the general linear group $GL_n(F)$ of degree n over the field F and the set $Z(M_n(F))$ of all zero-divisors of $M_n(F)$. Using the result and universal mapping property we prove that $M_n(F)$ is its total ring of fractions.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.401-417
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• 2017

Ever since their introduction, skew PBW ($Poincar{\acute{e}}$-Birkhoff-Witt) extensions of rings have kept growing in importance, as researchers characterized their properties (such as primeness, Krull and Goldie dimension, homological properties, etc.) in terms of intrinsic properties of the base ring, and studied their relations with other fields of mathematics, as for example quantum mechanics theory. Many rings and algebras arising in quantum mechanics can be interpreted as skew PBW extensions. Our aim in this paper is to study skew PBW extensions of Baer, quasi-Baer, principally projective and principally quasi-Baer rings, in the case when the base ring R is not assumed to be reduced. We just impose some mild compatibleness over the base ring R, and prove that these properties are stable over this kind of extensions.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.28 no.9
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• pp.551-554
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• 2015

This paper was analyzed electrical characteristics of super junction IGBT with super junction field rings. As a result of super junction IGBT with super junction field rings, we obtained 3,300 V breakdown voltage and good thermal characteristics. we obtained shrinked chip size because field ring was decreased than field ring for conventional IGBT, too. And we fabricated super junction IGBT with super junction field rings. As a result of measuring fabricated chip, we obtained 3,300 V breakdown voltage. The fabricated devices were replaced thyristos using high voltage conversion, sufficiently.