Relevant bibliographies by topics / Commutative ring; Localizations

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  1. Journal articles
  2. Dissertations / Theses
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  4. Book chapters

Academic literature on the topic 'Commutative ring; Localizations'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Commutative ring; Localizations"

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Angeleri Hügel, Lidia, Frederik Marks, Jan Št’ovíček, Ryo Takahashi, and Jorge Vitória. "Flat ring epimorphisms and universal localizations of commutative rings." Quarterly Journal of Mathematics 71, no. 4 (2020): 1489–520. http://dx.doi.org/10.1093/qmath/haaa041.

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Abstract We study different types of localizations of a commutative noetherian ring. More precisely, we provide criteria to decide: (a) if a given flat ring epimorphism is a universal localization in the sense of Cohn and Schofield; and (b) when such universal localizations are classical rings of fractions. In order to find such criteria, we use the theory of support and we analyse the specialization closed subset associated to a flat ring epimorphism. In case the underlying ring is locally factorial or of Krull dimension one, we show that all flat ring epimorphisms are universal localizations
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Tarizadeh, Abolfazl. "On flat epimorphisms of rings and pointwise localizations." MATHEMATICA 64 (87), no. 1 (2022): 129–38. http://dx.doi.org/10.24193/mathcluj.2022.1.14.

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We prove some new results on flat epimorphisms of commutative rings and pointwise localizations. Especially among them, it is proved that a ring $R$ is an absolutely flat (von-Neumann regular) ring if and only if it is isomorphic to the pointwise localization R^(-1)R, or equivalently, each R-algebra is R-flat. For a given minimal prime ideal p of a ring R, the surjectivity of the canonical map from R to R_p is characterized. Finally, we give a new proof to the fact that in a flat epimorphism of rings, the contraction-extension of an ideal equals the same ideal.
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Mustafa, Ibrahim, and Chnar Abdulkareem Ahmed. "ON NIL-SYMMETRIC RINGS AND MODULES SKEWED BY RING ENDOMORPHISM." Science Journal of University of Zakho 13, no. 3 (2025): 348–56. https://doi.org/10.25271/sjuoz.2025.13.3.1492.

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The symmetric property plays an important role in non-commutative ring theory and module theory. In this paper, we study the symmetric property with one element of the ring and two nilpotent elements of skewed by ring endomorphism on rings, introducing the concept of a right - -symmetric ring and extend the concept of right - -symmetric rings to modules by introducing another concept called the right - -symmetric module which is a generalization of -symmetric modules. According to this, we examine the characterization of a right - -symmetric ring and a right - -symmetric module and their relat
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Bremner, Murray. "Generalized Affine Kac-Moody Lie Algebras Over Localizations of the Polynomial Ring in One Variable." Canadian Mathematical Bulletin 37, no. 1 (1994): 21–28. http://dx.doi.org/10.4153/cmb-1994-004-8.

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AbstractWe consider simple complex Lie algebras extended over the commutative ring C[z,(z — a1)-1, . . . ,(z — an)-1] where a1, . . . ,an ∊ C. We compute the universal central extensions of these Lie algebras and present explicit commutation relations for these extensions. These algebras generalize the untwisted affine Kac-Moody Lie algebras, which correspond to the case n = 1, a1 = 0.
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Khashan, Hani, and Ece Celikel. "Weakly J-ideals of commutative rings." Filomat 36, no. 2 (2022): 485–95. http://dx.doi.org/10.2298/fil2202485k.

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Let R be a commutative ring with non-zero identity. In this paper, we introduce the concept of weakly J-ideals as a new generalization of J-ideals. We call a proper ideal I of a ring R a weakly J-ideal if whenever a,b ? R with 0 ? ab ? I and a ? J(R), then b ? I. Many of the basic properties and characterizations of this concept are studied. We investigate weakly J-ideals under various contexts of constructions such as direct products, localizations, homomorphic images. Moreover, a number of examples and results on weakly J-ideals are discussed. Finally, the third section is devoted to the cha
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FACCHINI, ALBERTO. "PURE-INJECTIVE ENVELOPE OF A COMMUTATIVE RING AND LOCALIZATIONS." Quarterly Journal of Mathematics 39, no. 3 (1988): 307–21. http://dx.doi.org/10.1093/qmath/39.3.307.

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Goodearl, K. R., and D. A. Jordan. "Localizations of injective modules." Proceedings of the Edinburgh Mathematical Society 28, no. 3 (1985): 289–99. http://dx.doi.org/10.1017/s0013091500017089.

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The question of whether an injective module E over a noncommutative noetherian ring R remains injective after localization with respect to a denominator set X⊆R is addressed. (For a commutative noetherian ring, the answer is well-known to be positive.) Injectivity of the localization E[X-1] is obtained provided either R is fully bounded (a result of K. A. Brown) or X consists of regular normalizing elements. In general, E [X-1] need not be injective, and examples are constructed. For each positive integer n, there exists a simple noetherian domain R with Krull and global dimension n+1, a left
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8

KHASHAN, Hani, and Ece YETKİN ÇELİKEL. "S-n-ideals of commutative rings." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 72, no. 1 (2023): 199–215. http://dx.doi.org/10.31801/cfsuasmas.1099300.

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Let $R$ be a commutative ring with identity and $S$ a multiplicatively closed subset of $R$. This paper aims to introduce the concept of $S-n$-ideals as a generalization of $n$-ideals. An ideal $I$ of $R$ disjoint with $S$ is called an $S-n$- ideal if there exists $s\in S$ such that whenever $ab \in I$ for $a,~b\in R,$ then $sa\in \sqrt{0}$ or $sb\in I$. The relationships among $S-n$-ideals, $n$-ideals, $S$-prime and $S$-primary ideals are clarified. Besides several properties, characterizations and examples of this concept, S-n-ideals under various contexts of constructions including direct p
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Ahmed, Chenar Abdul Kareem, and Saman Shafiq Othman. "On Right CNZ Rings with Involution." General Letters in Mathematics 14, no. 1 (2024): 17–24. http://dx.doi.org/10.31559/glm2024.14.1.3.

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The object of this paper is to present the notion of right CNZ rings with involutions, or, in short, right *-CNZ rings which are a generalization of right *-reversible rings and an extended of CNZ property . A ring R with involution * is called right *-CNZ if for any nilpotent elements x, y є R, xy = 0 implies yx * = 0. Every right *-CNZ ring with unity involution is CNZ but the converse need not be true in general, even for the commutative rings. In this note, we discussed some properties right *-CNZ ring. After that we explored right *-CNZ property on the extensions and localizations of the
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Axtell, M., S. J. Forman, and J. Stickles. "Properties of domainlike rings." Tamkang Journal of Mathematics 40, no. 2 (2009): 151–64. http://dx.doi.org/10.5556/j.tkjm.40.2009.464.

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In this paper we will examine properties of and relationships between rings that share some properties with integral domains, but whose definitions are less restrictive. If $R$ is a commutative ring with identity, we call $R$ a \textit{domainlike} ring if all zero-divisors of $R$ are nilpotent, which is equivalent to $(0)$ being primary. We exhibit properties of domainlike rings, and we compare them to presimplifiable rings and (hereditarily) strongly associate rings. Further, we consider idealizations, localizations, zero-divisor graphs, and ultraproducts of domainlike rings.
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Dissertations / Theses on the topic "Commutative ring; Localizations"

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HU, XIAO-MING, and 胡效銘. "Localization of commutative rings." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/03097490367752710004.

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碩士<br>國立中正大學<br>數學系研究所<br>104<br>Localization is a very useful tool in algebra. In commutative algebra, localization is a systematic method of adding multiplicative inverses to a ring. Suppose given a commutative ring R and a multiplicative system subset S. We want to construct a certain ring R and a ring homomorphism from R to R such that the image of S consists of in- vertible elements in R. We also want R to be the most ecient way to have this property. The localization of R at S is usually denoted by S^-
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Books on the topic "Commutative ring; Localizations"

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Jategaonkar, A. V. Localization in Noetherian Rings. Cambridge University Press, 2011.

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Jategaonkar, A. V. Localization in Noetherian Rings. Cambridge University Press, 2010.

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Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples. American Mathematical Society, 2021.

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Book chapters on the topic "Commutative ring; Localizations"

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Faye, Daouda, Mohamed Ben Fraj Ben Maaouia, and Mamadou Sanghare. "Localization in a Duo-Ring and Polynomials Algebra." In Non-Associative and Non-Commutative Algebra and Operator Theory. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32902-4_13.

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Yves, Diers. "Introduction." In Categories of Commutative Algebras. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198535867.003.0001.

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Abstract The motivation for a study of the properties of categories of commutative algebras was the natural outcome of the publication of several papers developing techniques which mimic those of classical commutative algebral and algebraic geometry in areas such as the study of ordered algebra, lattice algebra, real algebra, differential algebra, and C∞ -algebra. For instance, G. W. Brumfiel’s Partially ordered rings and semi-algebraic geometry [4] develops a kind of ordered commutative algebra, the paper by K. Keimel entitled ‘The representation of lattice ordered groups and rings by section
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Liu, Qing, and Reinie Erné. "Some topics incommutative algebra." In Algebraic Geometry and Arithmetic Curves. Oxford University PressOxford, 2002. http://dx.doi.org/10.1093/oso/9780198502845.003.0001.

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Abstract Unless otherwise specified, all rings in this book ,.will be supposed commutative and with unit. In this chapter, we introduce some indispensable basic notions of commutative algebra such as the tensor product, localization, and flatness. Other, more elaborate notions will be dealt with later, as they are needed. We assume that the reader is familiar with linear algebra over a commutative ring, and with Noetherian rings and modules.
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"6. Localization." In Topics in Commutative Ring Theory. Princeton University Press, 2007. http://dx.doi.org/10.1515/9781400828173-007.

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"Rings, Conditional Expectations, and Localization." In Commutative Ring Theory and Applications. CRC Press, 2017. http://dx.doi.org/10.1201/9780203910627-25.

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6

"Local Rings, DVRs, and Localization." In An Introduction to Commutative Algebra. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812562258_0002.

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Journal articles
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