• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1237-1246
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• 2022

In this paper, we introduce the concept of N-pure ideal as a generalization of pure ideal. Using this concept, a new and interesting type of rings is presented, we call it a mid ring. Also, we provide new characterizations for von Neumann regular and zero-dimensional rings. Moreover, some results about mp-ring are given. Finally, a characterization for mid rings is provided. Then it is shown that the class of mid rings is strictly between the class of reduced mp-rings (p.f. rings) and the class of mp-rings.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.429-442
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• 2023

In this paper, we introduce the concept of fuzzy ideals, anti-fuzzy ideals of Γ-BCK-algebras. We study the properties of fuzzy ideals, anti-fuzzy ideals of Γ-BCK-algebras. We prove that if f^-1(µ) is a fuzzy ideal of M, then µ is a fuzzy ideal of N, where f : M → N is an epimorphism of Γ-BCK-algebras M and N.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.295-304
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• 2016

In this paper we investigate the Artinianness of certain local cohomology modules $H^i_I(N)$ where N is a minimax module over a commutative Noetherian ring R and I is an ideal of R. Also, we characterize the set of attached prime ideals of $H^n_I(N)$, where n is the dimension of N.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-10
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• 2021

Let R and S be two commutative rings, J be an ideal of S and f : R → S be a ring homomorphism. The amalgamation of R and S along J with respect to f, denoted by R ⋈f J, is the special subring of R × S defined by R ⋈f J = {(a, f(a) + j) | a ∈ R, j ∈ J}. In this paper, we study some basic properties of a special kind of R ⋈f J-modules, called the amalgamation of M and N along J with respect to ��, and defined by M ⋈�� JN := {(m, ��(m) + n) | m ∈ M and n ∈ JN}, where �� : M → N is an R-module homomorphism. The new results generalize some known results on the amalgamation of rings and the duplication of a module along an ideal.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.251-262
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• 2012

Based on the theory of a falling shadow which was first formulated by Wang([14]), a theoretical approach of the ideal structure in BH-algebras is established. The notions of a falling subalgebra, a falling ideal, a falling strong ideal, a falling $n$-fold strong ideal and a falling translation ideal of a BH-algebra are introduced. Some fundamental properties are investigated. Relations among a falling subalgebra, a falling ideal and a falling strong ideal, a falling $n$-fold strong ideal are stated. A relation between a fuzzy subalgebra/ideal and a falling subalgebra/ideal is provided.

• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.181-191
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• 2018

In the present paper, we investigate the action of generalized derivation G associated with a derivation g in a (semi-) prime ring R satisfying $(G([x,y])-[G(x),y])^n=0$ for all x, $y{\in}I$, a nonzero ideal of R, where n is a fixed positive integer. Moreover, we also examine the above identity in Banach algebras.

• Journal of the Korean Society of Safety
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• v.20 no.2 s.70
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• pp.162-168
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• 2005

The lower flash points for the n-propanol+n-decane flammable mixture were measured by the Tag open-cup apparatus(ASTM D 1310). The experimental results of mixture exhibited the lower flash point than those of pure component in the flash point versus composition curve. The experimental value of the minimum flash point is $27^{\circ}C$ at a mole fraction of n-propanol of 0.71, and the flash point of n-propanol was $28^{\circ}C$. The experimentally obtained data were compared with the values that had been calculated by use of the prediction model, which assumes an ideal solution, and the flash point prediction models based on the van Laar equation were used to estimate the activity coefficients. The predictive curve based on an ideal solution deviated from the experimental data for this system. The experimental results demonstrate a close agreement with the predicted curves, which used the van Laar equation. The average absolute deviation(A.A.D.) from using the van Lau equation is $0.83^{\circ}C$. The methodology proposed here in this paper can thus be applied to incorporate an inherently safer design for chemical processes, such as determining safe storage and handling conditions for flammable solutions.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.439-450
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• 2019

Let R be a ring with unity. Given modules $M_R$ and $_RN$, $M_R$ is said to be absolutely $_RN$-pure if $M{\otimes}N{\rightarrow}L{\otimes}N$ is a monomorphism for every extension $L_R$ of $M_R$. For a module $M_R$, the subpurity domain of $M_R$ is defined to be the collection of all modules $_RN$ such that $M_R$ is absolutely $_RN$-pure. Clearly $M_R$ is absolutely $_RF$-pure for every flat module $_RF$, and that $M_R$ is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, $M_R$ is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. $R_R$ is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is $Pr{\ddot{u}}fer$ if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.

• Journal of the Korean Chemical Society
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• v.61 no.4
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• pp.139-142
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• 2017

Ethene ($C_2H_4$), which is produced in plants as they mature, was used to study its photoacoustic properties using photoacoustic spectroscopy. Detection of trace amounts, with $N_2$ gas, of $C_2H_4$ gas was also applied. The gas was tested in various conditions-temperature, concentration of the gas, gas cell length, and power of the laser- to determine their effect on the photoacoustic signal, the ideal conditions to detect trace gas amounts, and concentration of $C_2H_4$ produced by an avocado and a banana. A detection limit of 10 ppm was determined for pure $C_2H_4$. A detection of 5% and 13% (by volume) concentration of $C_2H_4$ was produced for a ripening avocado and banana, respectively, in closed space.

• Structural Engineering and Mechanics
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• v.42 no.3
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• pp.313-334
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• 2012

This paper examines the problem of a penny-shaped crack in a thermoporoelastic body. On the basis of the recently developed general solutions for thermoporoelasticity, appropriate potentials are suggested and the governing equations are solved in view of the similarity to those for pure elasticity. Exact and closed form fundamental solutions are expressed in terms of elementary functions. The singularity behavior is then discussed. The present solutions are compared with those in literature and an excellent agreement is achieved. Numerical calculations are performed to show the influence of the material parameters upon the distribution of the thermoporoelastic field. Due to its ideal property, the present solution is a natural benchmark to various numerical codes and simplified analyses.