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  • Title/Summary/Keyword: weak regularity

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ON WEAK II-REGULARITY AND THE SIMPLICITY OF PRIME FACTOR RINGS

  • Kim, Jin-Yong;Jin, Hai-Lan
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.1
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    • pp.151-156
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    • 2007
  • A connection between weak πregularity and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring R is weakly πregular if and only if every prime ideal is maximal. This result extends several known results nontrivially. Moreover a characterization of minimal prime ideals is also considered.

REGULARITY OF WEAK SOLUTIONS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

  • Choe, Hi-Jun;Jin, Bum-Ja
    • Journal of the Korean Mathematical Society
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    • v.40 no.6
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    • pp.1031-1050
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    • 2003
  • In this paper, we assume a density with integrability on the space L(0, T; Lq0) for some q0 and T > 0. Under the assumption on the density, we obtain a regularity result for the weak solutions to the compressible Navier-Stokes equations. That is, the supremum of the density is finite and the infimum of the density is positive in the domain T3 × (0, T). Moreover, Moser type iteration scheme is developed for L norm estimate for the velocity.

A STUDY ON WEAK BI-IDEALS OF NEAR-RINGS

  • Cho, Yong-Uk
    • East Asian mathematical journal
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    • v.24 no.2
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    • pp.145-149
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    • 2008
  • From the notion of bi-ideals in near-rings, various generalizations of regularity conditions have been studied. In this paper, we generalize further the notion of bi-ideals and introduce the notion of weak bi-ideals in near-rings and obtain some characterizations using this concept in left self distributive near-rings.

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ON ORDINALS

  • Chung, Se Hwa
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.4
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    • pp.675-686
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    • 2011
  • The aim of this paper is two fold: One of them is to introduce a formal definition of ordinals which is equivalent to Neumann's definition without assuming the axiom of regularity. The other is to introduce the weak transfinite set and show that the weak transfinite set is a transfinite limit ordinal.

REGULARITY RELATIVE TO A HEREDITARY TORSION THEORY FOR MODULES OVER A COMMUTATIVE RING

  • Qiao, Lei;Zuo, Kai
    • Journal of the Korean Mathematical Society
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    • v.59 no.4
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    • pp.821-841
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    • 2022
  • In this paper, we introduce and study regular rings relative to the hereditary torsion theory w (a special case of a well-centered torsion theory over a commutative ring), called w-regular rings. We focus mainly on the w-regularity for w-coherent rings and w-Noetherian rings. In particular, it is shown that the w-coherent w-regular domains are exactly the Prüfer v-multiplication domains and that an integral domain is w-Noetherian and w-regular if and only if it is a Krull domain. We also prove the w-analogue of the global version of the Serre-Auslander-Buchsbaum Theorem. Among other things, we show that every w-Noetherian w-regular ring is the direct sum of a finite number of Krull domains. Finally, we obtain that the global weak w-projective dimension of a w-Noetherian ring is 0, 1, or ∞.

WEAK BI-IDEALS OF NEAR-RINGS

  • Cho, Yong-Uk;Chelvam, T. Tamizh;Jayalakshmi, S.
    • The Pure and Applied Mathematics
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    • v.14 no.3
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    • pp.153-159
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    • 2007
  • The notion of bi-ideals in near-rings was effectively used to characterize the near-fields. Using this notion, various generalizations of regularity conditions have been studied. In this paper, we generalize further the notion of bi-ideals and introduce the notion of weak bi-ideals in near-rings and obtain various characterizations using the same in left self distributive near-rings.

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GLOBAL REGULARITY OF SOLUTIONS TO QUASILINEAR CONORMAL DERIVATIVE PROBLEM WITH CONTROLLED GROWTH

  • Kim, Do-Yoon
    • Journal of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1273-1299
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    • 2012
  • We prove the global regularity of weak solutions to a conormal derivative boundary value problem for quasilinear elliptic equations in divergence form on Lipschitz domains under the controlled growth conditions on the low order terms. The leading coefficients are in the class of BMO functions with small mean oscillations.

LOCALIZATION OF THE VORTICITY DIRECTION CONDITIONS FOR THE 3D SHEAR THICKENING FLUIDS

  • Yang, Jiaqi
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.6
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    • pp.1481-1490
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    • 2020
  • It is obtained that a localization of the vorticity direction coherence conditions for the regularity of the 3D shear thickening fluids to an arbitrarily small space-time cylinder. It implies the regularity of any geometrically constrained weak solution of the system considered independently of the type of the spatial domain or the boundary conditions.