• Honam Mathematical Journal
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• v.31 no.3
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• pp.429-436
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• 2009

In this short paper, we prove some new properties on homogeneous ideals and primary ideals of R(+)M.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.148-164
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• 2022

The main purpose of this paper is to apply the notion of hesitant fuzzy sets to an algebraic structure, so called a BCI-algebra. The primary goal of the study is to define hesitant fuzzy p-ideals and hesitant fuzzy quasi-associative ideals in BCI-algebras, and to investigate their properties and relations.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.221-233
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• 2009

In this article, we generalize a well-known result of Hebisch and Weinert that states that a finite semidomain is either zerosumfree or a ring. Specifically, we show that the class of commutative semirings S such that S has nonzero characteristic and every zero-divisor of S is nilpotent can be partitioned into zerosumfree semirings and rings. In addition, we demonstrate that if S is a finite commutative semiring such that the set of zero-divisors of S forms a subtractive ideal of S, then either every zero-sum of S is nilpotent or S must be a ring. An example is given to establish the existence of semirings in this latter category with both nontrivial zero-sums and zero-divisors that are not nilpotent.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.475-483
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• 2017

In this paper we consider the tight closure of an ideal relative to a module whose its zero submodule has a primary decomposition.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.855-867
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• 2001

This note we give a construction of a quotient ring $R/{\mu}$ induced via a fuzzy ideal ${\mu}$ in a ring R. The Fuzzy First, Second and Third Isomorphism Theorems are established. For some applications of this construction of quotient rings, we show that if ${\mu}$ is a fuzzy ideal of a commutative ring R, then $\mu$ is prime (resp. $R/{\mu}$ is a field, every zero divisor in $R/{\mu}$ is nilpotent). Moreover we give a simpler characterization of fuzzy maximal ideal of a ring.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.117-126
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• 2020

Let R be a commutative ring with identity. A proper ideal I of R is called 2-prime if for all a, b ∈ R such that ab ∈ I, then either a² or b² lies in I. In this paper, we study 2-prime ideals which are generalization of prime ideals. Our study provides an analogous to the prime avoidance theorem and some applications of this theorem. Also, it is shown that if R is a PID, then the families of primary ideals and 2-prime ideals of R are identical. Moreover, a number of examples concerning 2-prime ideals are given. Finally, rings in which every 2-prime ideal is a prime ideal are investigated.

• Proceedings of the KIEE Conference
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• 2008.04c
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• pp.9-12
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• 2008

Mathematical singularities of circuit equations with three-phase ideal transformer connections are studied. Three-wired wye-wye connections, delta-delta connections, and primary four-wired wye-delta connections are singular. The matrices of their circuit equations have zeros in their eigenvalues. Three-wired wye-delta connections, wye-wye-delta connections, and primary four-wired wye-wye connections are not singular. The physical meaning of their singularities is that they are sensitive and prone to be ill-conditioned. Equivalent shunt admittances representing ion losses and magnetizing inductances make the singular matrices non-singular in wye-connected circuits. And, equivalent series impedances representing copper losses and leakage inductances make the singular matrices non-singular in delta-connected circuits. The tableau analysis is used for the study.

• Journal of Chest Surgery
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• v.28 no.2
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• pp.156-161
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• 1995

Although there are many kinds of method in treatment of tracheal stenosis, tracheal resection and primary anastomosis can be performed for management of various kinds of tracheal stenosis because it is considered the most anatomical ideal therapeutic modality. During a 10-year period we performed 18 tracheal resection on 18 patients with no operative mortality and some morbidity. 13 patients had tracheal stenosis caused by endotracheal intubation [eight patients or tracheostomy [five patients ; and five patients caused by a variety of neoplastic lesions [four primary and one secondary . The length of tracheal stenosis were various from 1.5cm to 5.5cm and site of tracheal stenosis were cervical[17patients and thoracic [one patient . Operative techniques were tracheal resection and primary anastomosis[18 patients and additional procedures were cricoid cartilage reconstruction with costal cartilage [one patient , primary repair of esophagus[one patient and suprahyoid laryngeal release technique[eight patients without any complications. We have eight complications; tracheal restenosis were developed in five patients[growth of grannulation tissue at anastomotic site in three patients, delayed restenosis in two patients , anastomotic disruption in one patient, hoarseness and pneumonia in each of two patients. We managed tracheal complications with T-tube insertion in two patients, permanent tracheostomy in three patients and insertion of Gianturco tracheal stent in one patient, but tracheal stent did not reveal good result because it caused persistent production of sputum. We concluded that it is necessary to access full length of normal trachea including suprahyoid laryngeal release technique to avoid anastomotic tension in tracheal surgery and develope new ideal techniques to manage postoperative tracheal complications, because we suppose tracheal complications are developed due to anastomotic tension.

• Proceedings of the Korean Society of Food Hygiene and Safety Conference
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• 2002.05a
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• pp.147-147
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• 2002

This experimental study was carried out to investigate on the safety of Nog-yong aqua-acupuncture solution in primary culture of adult rat hepatocytes. Primary culture of adult rat hepatocytes has been considered as a ideal model for toxicological studies because cultured hepatocytes maintained many liver-specific functions. In this research, we investigated the effects of Nog-yong aqua-aqupunture(1-10$\mu\textrm{g}$/ml) on cytotoxicites in primary culture of adult rat hepatocytes using LDH release assays. Hepatic glutathione level. glutathione-S-transferase activity, and albumin synthesis were not affected by treatment with Nog-yong aqua-aqupuntur alone. Nog-yong aqua-aqupuncoure solution(0.5-$10{\mu}\textrm{g}$/ml) on cytotoxicites in primary culture of adult rat hepatocytes using LDH release not significantly affected normal functional charaterists.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.549-582
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• 2016

All rings are commutative with $1{\neq}0$ and n is a positive integer. Let ${\phi}:{\Im}(R){\rightarrow}{\Im}(R){\cup}\{{\emptyset}\}$ be a function where ${\Im}(R)$ denotes the set of all ideals of R. We say that a proper ideal I of R is ${\phi}$-n-absorbing primary if whenever $a_1,a_2,{\cdots},a_{n+1}{\in}R$ and $a_1,a_2,{\cdots},a_{n+1}{\in}I{\backslash}{\phi}(I)$, either $a_1,a_2,{\cdots},a_n{\in}I$ or the product of $a_{n+1}$ with (n-1) of $a_1,{\cdots},a_n$ is in $\sqrt{I}$. The aim of this paper is to investigate the concept of ${\phi}$-n-absorbing primary ideals.