Results 231 to 240 of about 1,487,509 (274)

On the Rings of Valuation Vectors

The Annals of Mathematics, 1953
Let {R,,,} be a system of topological rings and Qa open subrings of Ra . We consider the set R of all vectors a = (aa), where aa are elements in Ra and which belong to Qa, except for a finite number of a. By the usual definition of component-wise addition and multiplication, R forms a ring containing the direct sum 0 of all Qa .
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Valuations and Prufer Rings

Canadian Journal of Mathematics, 1974
The word ring is used to mean commutative ring. Just as valuations on fields are used to study domains, so valuations on rings can be used to study rings; these rings need not have units [12]. We introduce slightly weaker conditions than having identity in order to get a more general theory.
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The homology of SL2 of discrete valuation rings

Advances in Mathematics, 2022
Kevin Hutchinson, B. Mirzaii, F. Mokari
semanticscholar   +1 more source

REAL CLOSED RINGS AND ORDERED VALUATION RING

Mathematical Logic Quarterly, 1983
The article contains some model theoretic results on real closed rings and ordered valuation rings, supplementing the work of Cherlin and Dickmann on the same subject. The results confirm the analogy between real closed rings and real closed fields. There is a minor error in Proposition 1.9 which is part of Theorem 1.
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Generalized Discrete Valuation Rings

Canadian Journal of Mathematics, 1969
Jategaonkar (5) has constructed a class of rings which can be used to provide counterexamples to problems concerning unique factorization in non-commutative domains, the left-right symmetry of the global dimension for a right- Noetherian ring and the transhnite powers of the Jacobson radical of a right- Noetherian ring.
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A Note on Henselian Valuation Rings

Canadian Mathematical Bulletin, 1968
Let K be a field and Ka its algebraic closure. A valuation a ring A of K is called henselian, if there is only one valuation ring C of Ka which lies over A (i.e. such that C ∩ K = A) or, equivalently, if Hensel's Lemma is valid for K, A (see [5], F). In the following, we shall consider only rank one valuation rings.
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Noncommutative valuation rings

1984
Translation from Tr. Mosk. Mat. O.-va 45, 265-280 (Russian) (1982; Zbl 0531.16011).
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Filtration on a Ring Make a Quasi Valuation or Valuation Ring

2015
In this paper we show that if R is a filtered ring then we can define a quasi valuation ring. And there exists a valuation ring if R is some kind of filtered ring. Then we prove some properties and relations between filtered ring and quasi valuation ring and valuation ...
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Global Krull Dimension and Global Dual Krull Dimension of Valuation Rings

abelian groups, module theory, and topology, 2019
T. Albu, P. Vámos
semanticscholar   +1 more source

Valuation rings are derived splinters

Mathematische Zeitschrift, 2021
Rankeya Datta, Benjamin Antieau
exaly