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1.
Niels Schwartz 《manuscripta mathematica》2000,102(3):347-381
The paper contributes to the investigation of epimorphisms in the category of reduced partially ordered rings (porings). Two main questions are considered: 1) Does the set of isomorphism classes of a given poring have a largest element (an epimorphic hull)? 2) Given an epimorphic extension, or even a Prüfer extension, f:A→B of porings: how closely are A and B related to each other? Received: 17 June 1999 相似文献
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Carmelo Antonio Finocchiaro 《代数通讯》2017,45(10):4521-4527
Using the general approach to invertibility for ideals in ring extensions given by Knebush and Zhang in [9], we investigate about connections between faithfully flatness and invertibility for ideals in rings with zero divisors. 相似文献
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Jorge Martinez 《代数通讯》2013,41(9):3479-3488
Abstract As defined by Nicholson [Nicholson, W. K. (1977). Lifting idempotents and exchange rings. Trans. Amer. Math. Soc. 229:269–278] an element of a ring R is clean if it is the sum of a unit and an idempotent, and a subset A of R is clean if every element of A is clean. It is shown that a semiprimitive Gelfand ring R is clean if and only if Max(R) is zero-dimensional; if and only if for each M ∈ Max(R), the intersection all prime ideals contained in M is generated by a set of idempotents. We also give several equivalent conditions for clean functional rings. In fact, a functional ring R is clean if and only if the set of clean elements is closed under sum; if and only if every zero-divisor is clean; if and only if; R has a clean prime ideal. 相似文献
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Archiv der Mathematik - In this article, we show that the homotopy invariance of K-theory holds for rings of weak global dimension at most one. Prüfer domains are examples of such rings. We... 相似文献
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Yu. L. Ershov 《Algebra and Logic》2001,40(3):144-158
We study into questions that naturally arise when Prüfer rings are viewed from the geometry standpoint. A ring of principal ideals which has infinitely many prime ideals and is such that its field of fractions is non-Hilbertian is constructed. This answers in the negative a question of Lang. 相似文献
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We prove that Vaught’s conjecture is true for modules over a commutative Prüfer ring. It is shown that a positive solution
to Vaught’s conjecture for modules over 1-dimensional Noetherian domains would imply the same for modules over finitely presented
algebras.
This article was written during the visit of the second author to the University of Manchester supported by EPSRC grant GR/L68827.
She would like to thank the University for hospitality.
Translated fromAlgebra i Logika, Vol. 38, No. 4, pp. 419–435, July–August, 1999. 相似文献
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In this article, it is proved that a domain R is a Prüfer domain if and only if it is coherent, integrally closed and FP-id R (R) ≤ 1. 相似文献
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In this paper we characterize the (commutative) Priifer rings that can be realized as endomorphism rings of artinian modules over arbitrary associative rings with identity (Theorem 4.7). This characterization is obtained by determining the structure of ∑-pure-injective modules over Prufer rings (Theorems 3.4 and 3.5) 相似文献
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《代数通讯》2013,41(4):1633-1642
Abstract Let D be an integral domain, S ? D a multiplicative set such that aD S ∩ D is a principal ideal for each a ∈ D and let D (S) = ? s∈S D[X/s]. It is known that if D is a Prüfer v-multiplication domain (resp., generalized GCD domain, GCD domain), then so is D (S) respectively. When D is a Noetherian domain, we obtain a similar result for the power series analog D ((S)) = ? s∈S D[[X/s]] of D (S). Our approach takes care simultaneously of both cases D (S) and D ((S)). 相似文献
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In this paper we consider six Prüfer-like conditions on a commutative ring R, and introduce seventh condition by defining the ring R to be maximally Prüfer if R M is Prüfer for every maximal ideal M of R, and we show that the class of such rings lie properly between Prüfer rings and locally Prüfer rings. We give a characterization of such rings in terms of the total quotient ring and the core of the regular maximal ideals. We also find a relationship of such rings with strong Prüfer rings. 相似文献
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One of the most important results of Chevalley's extension theorem states that every valuation domain has at least one extension to every extension field of its quotient field. We state a generalization of this result for Prüfer domains with any finite number of maximal ideals. Then we investigate extensions of semilocal Prüfer domains in algebraic field extensions. In particular, we find an upper bound for the cardinality of extensions of a semilocal Prüfer domain. Moreover, we show that any two extensions of a semilocal Prüfer domain are incomparable (by inclusion) in an algebraic extension of fields. 相似文献
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We examine in this paper some properties of Morita and Prüfer hulls of FCP and FIP extensions of rings. Dichotomy phenomena appear in the case of a quasi-local base ring. In the general case, we define relative supports that allow us to introduce the concept of direct factorization of an extension and to characterize these hulls. 相似文献
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Rachida El Khalfaoui 《代数通讯》2020,48(9):3800-3810
AbstractIn this article, we define the ?-Krull dimension as a generalization of Krull dimension. This property is treated here as a part of a study on some constractions of rings such as direct products, amalgamation of rings, and trivial ring extensions. 相似文献
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Yiqiang Zhou 《代数通讯》2013,41(9):3199-3212
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Demetrios Brizolis 《代数通讯》2013,41(10):1065-1077