共查询到20条相似文献,搜索用时 15 毫秒
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We introduce a naive notion of a system of parameters for a homologically finite complex over a commutative noetherian local ring and compare it to the system of parameters defined by Christensen. We show that these notions differ in general but that they agree when the complex in question is a DG R-algebra. In this case we also show that the Krull dimension defined in terms of the lengths of such systems of parameters agrees with Krull dimensions defined in terms of certain chains of prime ideals. 相似文献
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K. I. Beidar E. R. Puczylowski P. F. Smith 《Proceedings of the American Mathematical Society》1997,125(2):355-361
Let be a ring with involution and invertible 2, and let be the subring of generated by the symmetric elements in . The following questions of Lanski are answered positively:
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- Must have Krull dimension when does?
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- Is every Artinian -module Artinian as an -module?
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V. V. Tenzina 《Journal of Mathematical Sciences》2006,139(4):6803-6813
In this paper, we introduce a topological analog of Krull dimension. We are interested in particular properties of rings and
modules having topological Krull dimension. The topological Baer radical of a PI-ring possessing a module with topological
Krull dimension will be investigated.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 215–230, 2004. 相似文献
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We shall define localic Krull dimension for topological spaces. In particular, a space X has the localic Krull dimension n if n is the greatest number such that X can be mapped, via a continuous and open map, onto the n-chain seen as an Alexandroff space. We shall discuss the applications of this concept in obtaining topological completeness results in modal logic. We shall also show how the localic Krull dimension is related to the Krull dimension in ring theory. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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A. I. Generalov 《Journal of Mathematical Sciences》1999,95(2):2088-2095
For a right Noetherian serial ring R that is not Artinian, it is proved that the Krull dimension of the category of finitely generated right R-modules is equal to one. Bibliography: 17titles.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 236, 1997, pp. 73–86. 相似文献
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Let \(R\) be an APVD with maximal ideal \(M\) . We show that the power series ring \(R[[x_1,\ldots ,x_n]]\) is an SFT-ring if and only if the integral closure of \(R\) is an SFT-ring if and only if ( \(R\) is an SFT-ring and \(M\) is a Noether strongly primary ideal of \((M:M)\) ). We deduce that if \(R\) is an \(m\) -dimensional APVD that is a residually *-domain, then dim \(R[[x_1,\ldots ,x_n]]\,=\,nm+1\) or \(nm+n\) . 相似文献
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Sophie Frisch 《Proceedings of the American Mathematical Society》1996,124(12):3595-3604
If is a subring of a Krull ring such that is a valuation ring for every finite index , in Spec, we construct polynomials that map into the maximal possible (for a monic polynomial of fixed degree) power of , for all in Spec simultaneously. This gives a direct sum decomposition of Int, the -module of polynomials with coefficients in the quotient field of that map into , and a criterion when Int has a regular basis (one consisting of 1 polynomial of each non-negative degree).
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E. Rtveliashvili 《Georgian Mathematical Journal》1996,3(3):263-274
The Krull dimension of rings of skew polynomials is studied. Earlier the problem of Krull dimension was investigated only for some particular cases, namely, for Weyl algebras [2], a ring of differential operators [7,8], as well as for rings of Laurent skew polynomials [9–10]. 相似文献