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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

On the transfer of some $t-$locally properties

Omar OUZZAOUIT
Ali TAMOUSSIT
Sayfa
825–832
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

A particular attention is devoted to the transfer of almost Krull and locally P$v$MD properties to integral closure of a domain having the same property.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we study the transfer of some $t$-locally properties which are stable under localization to $t$-flat overrings of an integral domain $D$.
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Temel Bulgular & Veri:We show that $D,$ $D[X],$ $D\langle X\rangle,$ $D(X)$ and $D[X]_{N_v}$ are simultaneously $t$-locally P$v$MDs (resp., $t$-locally Krull, $t$-locally G-GCD, $t$-locally Noetherian, $t$-locally Strong Mori).
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Sonuç & Katkı:A particular attention is devoted to the transfer of almost Krull and locally P$v$MD properties to integral closure of a domain having the same property.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:$t$--Flat overring · ($t$--)Nagata ring · Serre conjecture ring

Abstract

In this paper, we study the transfer of some $t$-locally properties which are stable under localization to $t$-flat overrings of an integral domain $D$. We show that $D,$ $D[X],$ $D\langle X\rangle,$ $D(X)$ and $D[X]_{N_v}$ are simultaneously $t$-locally P$v$MDs (resp., $t$-locally Krull, $t$-locally G-GCD, $t$-locally Noetherian, $t$-locally Strong Mori). A complete characterization of when a pullback is a $t$-locally P$v$MD (resp., $t$-locally GCD, $t$-locally G-GCD, $t$-locally Noetherian, $t$-locally Strong Mori, $t$-locally Mori) is given. As corollaries, we investigate the transfer of some $t$-locally properties among domains of the form $D+XK[X]$, $D+XK[[X]]$ and amalgamated algebras. A particular attention is devoted to the transfer of almost Krull and locally P$v$MD properties to integral closure of a domain having the same property.

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Bu Makaleye Atıf Yap

OUZZAOUIT, O., TAMOUSSIT, A. (2022). On the transfer of some $t-$locally properties. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 825–832. https://ajindex.com/articles/529501

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Kaynakça (2)

  1. D.D. Anderson, D.F. Anderson and R. Markanda, The rings $R(X)$ and $R\langle X\rangle$, J. Algebra, 95, 96–115, 1985 [2] J.T. Arnold, On the ideal theory of the Kronecker function ring and the domain $D(X)$, Canad. J. Math. 21, 558–563, 1969. [3] M. D’Anna, C.A. Finocchiaro and M. Fontana, Amalgamated algebras along an ideal, in: Commutative Algebra and Applications, Walter de Gruyter, Berlin, 155–172, 2009. [4] D.E. Dobbs, E. Houston, T. Lucas and M. Zafrullah, $t$–Linked overrings and Prüfer $v$–multiplication domains, Comm. Algebra, 17 (11), 2835–2852, 1989. [5] S. El Baghdadi, On a class of Prüfer v–multiplication domains, Comm. Algebra, 30, 3723–3742, 2002. [6] M. Fontana and S. Gabelli, On the class group and the local class group of a pullback, J. Algebra, 181, 803–835, 1996. [7] M. Fontana, S. Gabelli and E. Houston, UMT-domains and domains with Prüfer integral closure, Comm. Algebra, 26, 1017–1039, 1998. [8] S. Gabelli and E. Houston, Coherent-like conditions in pullbacks, Michigan Math. J. 44, 99–122, 1997. [9] S. Gabelli and E.G. Houston, Ideal theory in pullbacks, in: Non-Noetherian Com- mutative Ring Theory, in: Math. Appl. 520, 199–227,
  2. Kluwer Academic, Dordrecht, 2000. [10] W. Heinzer, Some properties of integral closure, Proc. Am. Math. Soc. 18, 749–753, 1967. [11] B.G. Kang, Prüfer v–multiplication domains and the ring $R[X]_{N_v}$, J. Algebra 123, 151-170, 1989. [12] D.J. Kwak and Y.S. Park, On $t$–flat overrings, Chinese J. Math. 23, 17–24, 1995. [13] F. Lucius, Rings with a theory of greatest common divisors, Manuscripta Math. 95, 117–136, 1998. [14] A. Mimouni, TW–domains and Strong Mori domains, J. Pure Appl. Algebra, 177, 79–93, 2003. [15] E.M. Pirtle, Integral domains which are almost Krull, J. Sci. Hiroshima Univ. Ser. A-I Math. 32 (2), 441–447, 1968. [16] F. Richman, Generalized quotient rings, Proc. Amer. Math. Soc. 16, 794–799, 1965.