• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.373-397
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• 2024

Lambek introduced the concept of symmetric rings to expand the commutative ideal theory to noncommutative rings. In this study, we propose an extension of symmetric rings called strongly α-symmetric rings, which serves as both a generalization of strongly symmetric rings and an extension of symmetric rings. We define a ring R as strongly α-symmetric if the skew polynomial ring R[x; α] is symmetric. Consequently, we provide proofs for previously established outcomes regarding symmetric and strongly symmetric rings, directly derived from the results we have obtained. Furthermore, we explore various properties and extensions of strongly α-symmetric rings.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.853-868
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• 2022

We study the structure of right regular commutators, and call a ring R strongly C-regular if ab - ba ∈ (ab - ba)²R for any a, b ∈ R. We first prove that a noncommutative strongly C-regular domain is a division algebra generated by all commutators; and that a ring (possibly without identity) is strongly C-regular if and only if it is Abelian C-regular (from which we infer that strong C-regularity is left-right symmetric). It is proved that for a strongly C-regular ring R, (i) if R/W(R) is commutative, then R is commutative; and (ii) every prime factor ring of R is either a commutative domain or a noncommutative division ring, where W(R) is the Wedderburn radical of R.

• East Asian mathematical journal
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• v.22 no.1
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• pp.61-69
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• 2006

A near-ring N is reduced if, for $a{\in}N,\;a^2=0$ implies a=0, and N is left strongly regular if for all $a{\in}N$ there exists $x{\in}N$ such that $a=xa^2$. Mason introduced this notion and characterized left strongly regular zero-symmetric unital near-rings. Several authors ([2], [5], [7]) studied these properties in near-rings. Reddy and Murty extended some results in Mason to the non-zero symmetric case. In this paper, we will define a concept of strong reducedness and investigate a relation between strongly reduced near-rings and left strongly regular near-rings.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.669-677
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• 2013

In this paper we introduce the notion of NI near-rings similar to the notion introduced in rings. We give topological properties of collection of strongly prime ideals in NI near-rings. We have shown that if N is a NI and weakly pm near-ring, then $Max(N)$ is a compact Hausdorff space. We have also shown that if N is a NI near-ring, then for every $a{\in}N$, $cl(D(a))=V(N^*(N)_a)=Supp(a)=SSpec(N){\setminus}int\;V(a)$.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.483-488
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• 2012

In this paper we introduce the notion of P-strongly regular near-ring. We have shown that a zero-symmetric near-ring N is P-strongly regular if and only if N is P-regular and P is a completely semiprime ideal. We have also shown that in a P-strongly regular near-ring N, the following holds: (i) $Na$ + P is an ideal of N for any $a{\in}N$. (ii) Every P-prime ideal of N containing P is maximal. (iii) Every ideal I of N fulfills I + P = $I^2$ + P.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.529-545
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• 2022

This article concerns a ring property that arises from combining one-sided duo factor rings and centers. A ring R is called right CIFD if R/I is right duo by some proper ideal I of R such that I is contained in the center of R. We first see that this property is seated between right duo and right π-duo, and not left-right symmetric. We prove, for a right CIFD ring R, that W(R) coincides with the set of all nilpotent elements of R; that R/P is a right duo domain for every minimal prime ideal P of R; that R/W(R) is strongly right bounded; and that every prime ideal of R is maximal if and only if R/W(R) is strongly regular, where W(R) is the Wedderburn radical of R. It is also proved that a ring R is commutative if and only if D₃(R) is right CIFD, where D₃(R) is the ring of 3 by 3 upper triangular matrices over R whose diagonals are equal. Furthermore, we show that the right CIFD property does not pass to polynomial rings, and that the polynomial ring over a ring R is right CIFD if and only if R/I is commutative by a proper ideal I of R contained in the center of R.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.217-232
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• 2016

We make a study of two generalizations of regular rings, concentrating our attention on the structure of idempotents. A ring R is said to be right attaching-idempotent if for $a{\in}R$ there exists $0{\neq}b{\in}R$ such that ab is an idempotent. Next R is said to be generalized regular if for $0{\neq}a{\in}R$ there exist nonzero $b{\in}R$ such that ab is a nonzero idempotent. It is first checked that generalized regular is left-right symmetric but right attaching-idempotent is not. The generalized regularity is shown to be a Morita invariant property. More structural properties of these two concepts are also investigated.

• Journal of the Optical Society of Korea
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• v.16 no.4
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• pp.425-431
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• 2012

Utilizing the three-dimensional Snyder-Mitchell model with a PT-symmetric potential, we study the influence of PT symmetry on beam propagation in strongly nonlocal nonlinear media. The complex Coulomb potential is used as the PT-symmetric potential. A localized spatiotemporal accessible soliton solution of the model is obtained. Specific values of the modulation depth for different soliton parameters are discussed. Our results reveal that in these media the localized solitons can exist in various shapes, such as single-layer and multi-layer disk-shaped structures, as well as vortex-ring and necklace patterns.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.151-154
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• 2002

The twin impulse wave leads to very complicated flow fields, such as Mach stem, spherical waves, and vortex ring. The twin impulse wave discharged from the exits of the two tubes placed in parallel is investigated to understand detailed flow physics associated with the twin impulse wave, compared with those in a single impulse wave. In the current study, the merging phenomena and propagation characteristics of the impulse waves are investigated using a shock tube experiment and by numerical computations. The Harten-Yee's total variation diminishing (TVD) scheme is used to solve the unsteady, two-dimensional, compressible, Euler equations. The Mach number $M_{s}$, of incident shock wave is changed below 1.5 and the distance between two-parallel tubes, L/d, is changed from 1.2 to 4.0. In the shock tube experiment, the twin impulse waves are visualized by a Schlieren optical system for the purpose of validation of computational work. The results obtained show that on the symmetric axis between two parallel tubes, the peak pressure produced by the twin-impulse waves and its location strongly depend upon the distance between two parallel tubes, L/d and the incident shock Mach number, $M_{s}$. The predicted Schlieren images represent the measured twin-impulse wave with a good accuracy.

• Journal of Astronomy and Space Sciences
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• v.28 no.1
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• pp.27-36
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• 2011

The present study examines the morning-afternoon asymmetry of the geosynchronous magnetic field strength on the dayside (magnetic local time [MLT] = 06:00~18:00) using observations by the Geostationary Operational Environmental Satellites (GOES) over a period of 9 years from February 1998 to January 2007. During geomagnetically quiet time (Kp < 3), we observed that a peak of the magnetic field strength is skewed toward the earlier local times (11:07~11:37 MLT) with respect to local noon and that the geosynchronous field strength is larger in the morning sector than in the afternoon sector. That is, there is the morning-afternoon asymmetry of the geosynchronous magnetic field strength. Using solar wind data, it is confirmed that the morning-afternoon asymmetry is not associated with the aberration effect due to the orbital motion of the Earth about the Sun. We found that the peak location of the magnetic field strength is shifted toward the earlier local times as the ratio of the magnetic field strength at MLT = 18 (B-dusk) to the magnetic field strength at MLT = 06 (B-dawn) is decreasing. It is also found that the dawn-dusk magnetic field median ratio, B-dusk/B-dawn, is decreasing as the solar wind dynamic pressure is increasing. The morning-afternoon asymmetry of the magnetic field strength appears in Tsyganenko geomagnetic field model (TS-04 model) when the partial ring current is included in TS-04 model. Unlike our observations, however, TS-04 model shows that the peak location of the magnetic field strength is shifted toward local noon as the solar wind dynamic pressure grows in magnitude. This may be due to that the symmetric magnetic field associated with the magnetopause current, strongly affected by the solar wind dynamic pressure, increases. However, the partial ring current is not affected as much as the magnetopause current by the solar wind dynamic pressure in TS-04 model. Thus, our observations suggest that the contribution of the partial ring current at geosynchronous orbit is much larger than that expected from TS-04 model as the solar wind dynamic pressure increases.