• Title/Summary/Keyword: maximal regularity

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REMARKS ON CURVES OF MAXIMAL REGULARITY IN ℙ3

  • Lee, Wanseok
    • East Asian mathematical journal
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    • v.36 no.3
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    • pp.349-357
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    • 2020
  • For a nondegenerate projective curve C ⊂ ℙr of degree d, it was shown that the Castelnuovo-Mumford regularity reg(C) of C is at most d - r + 2. And the curves of maximal regularity which attain the maximally possible value d - r + 2 are completely classified. In this short note, we first collect several known results about curves of maximal regularity. We provide a new proof and some partial results. Finally we suggest some interesting questions.

FURTHER STUDY OF RINGS IN WHICH ESSENTIAL MAXIMAL RIGHT IDEALS ARE GP-INJECTIVE

  • SANGBOK NAM;TAEHEE LEE;HWAJOON KIM
    • Journal of applied mathematics & informatics
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    • v.41 no.6
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    • pp.1173-1180
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    • 2023
  • In this paper, rings in which essential maximal right ideals are GP-injective are studied. Whether the rings with this condition satisfy von Neumann regularity is the goal of this study. The obtained research results are twofold: First, it was shown that this regularity holds even when the reduced ring is replaced with π-IFP and NI-ring. Second, it was shown that this regularity also holds even when the maximal right ideal is changed to GW-ideal. This can be interpreted as an extension of the existing results.

ON THE MINIMAL FREE RESOLUTION OF CURVES OF MAXIMAL REGULARITY

  • Lee, Wanseok;Park, Euisung
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.6
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    • pp.1707-1714
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    • 2016
  • Let $C{\subset}{\mathbb{P}}^r$ be a nondegenerate projective curve of degree d > r + 1 and of maximal regularity. Such curves are always contained in the threefold scroll S(0, 0, r - 2). Also some of such curves are even contained in a rational normal surface scroll. In this paper we study the minimal free resolution of the homogeneous coordinate ring of C in the case where $d{\leq}2r-2$ and C is contained in a rational normal surface scroll. Our main result provides all the graded Betti numbers of C explicitly.

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 ${\pi}-regularity$ and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring R is weakly ${\pi}-regular$ 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.

FUZZY COMPACTNESS, FUZZY REGULARITY VIA FUZZY MAXIMAL OPEN AND FUZZY MINIMAL CLOSED SETS

  • SWAMINATHAN, A.;SIVARAJA, S.
    • Journal of applied mathematics & informatics
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    • v.40 no.1_2
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    • pp.185-190
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    • 2022
  • The aim of this article is to define fuzzy maximal open cover and discuss its few properties. we also defined and study fuzzy m-compact space and discussed its properties. Also we obtain few more results on fuzzy minimal c-regular and fuzzy minimal c-normal spaces. We have proved that a fuzzy Haussdorff m-compact space is fuzzy minimal c-normal.

ON RINGS WHOSE ESSENTIAL MAXIMAL RIGHT IDEALS ARE GP-INJECTIVE

  • Jeong, Jeonghee;Kim, Nam Kyun
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.399-407
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    • 2022
  • In this paper, we continue to study the von Neumann regularity of rings whose essential maximal right ideals are GP-injective. It is proved that the following statements are equivalent: (1) R is strongly regular; (2) R is a 2-primal ring whose essential maximal right ideals are GP-injective; (3) R is a right (or left) quasi-duo ring whose essential maximal right ideals are GP-injective. Moreover, it is shown that R is strongly regular if and only if R is a strongly right (or left) bounded ring whose essential maximal right ideals are GP-injective. Finally, we prove that a PI-ring whose essential maximal right ideals are GP-injective is strongly π-regular.

DEGENERATE VOLTERRA EQUATIONS IN BANACH SPACES

  • Favini, Angelo;Tanabe, Hiroki
    • Journal of the Korean Mathematical Society
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    • v.37 no.6
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    • pp.915-927
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    • 2000
  • This paper is concerned with degenerate Volterra equations Mu(t) + ∫(sub)0(sup)t k(t-s) Lu(s)ds = f(t) in Banach spaces both in the hyperbolic case, and the parabolic one. The key assumption is played by the representation of the underlying space X as a direct sum X = N(T) + R(T), where T is the bounded linear operator T = ML(sup)-1. Hyperbolicity means that the part T of T in R(T) is an abstract potential operator, i.e., -T(sup)-1 generates a C(sub)0-semigroup, and parabolicity means that -T(sup)-1 generates an analytic semigroup. A maximal regularity result is obtained for parabolic equations. We will also investigate the cases where the kernel k($.$) is degenerated or singular at t=0 using the results of Pruss[8] on analytic resolvents. Finally, we consider the case where $\lambda$ is a pole for ($\lambda$L + M)(sup)-1.

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