-spaces of conjugate systems on local fields
Jia Chao (1974)
Studia Mathematica
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Jia Chao (1974)
Studia Mathematica
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Najib Mahdou (2017)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, we are concerned with G-rings. We generalize the Kaplansky’s theorem to rings with zero-divisors. Also, we assert that if is a ring extension such that for some regular element of , then is a G-ring if and only if so is . Also, we examine the transfer of the G-ring property to trivial ring extensions. Finally, we conclude the paper with illustrative examples discussing the utility and limits of our results.
Teo Mora (1989)
Publications mathématiques et informatique de Rennes
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Abdelhafed Elkhadiri (2011)
Annales Polonici Mathematici
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Let R be a real closed field, and denote by the ring of germs, at the origin of Rⁿ, of functions in a neighborhood of 0 ∈ Rⁿ. For each n ∈ ℕ, we construct a quasianalytic subring with some natural properties. We prove that, for each n ∈ ℕ, is a noetherian ring and if R = ℝ (the field of real numbers), then , where ₙ is the ring of germs, at the origin of ℝⁿ, of real analytic functions. Finally, we prove the Real Nullstellensatz and solve Hilbert’s 17th Problem for the ring . ...
A. A. Mehrvarz, R. Naghipour, M. Sedghi (2006)
Colloquium Mathematicae
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Let Φ be a system of ideals on a commutative Noetherian ring R, and let S be a multiplicatively closed subset of R. The first result shows that the topologies defined by and are equivalent if and only if S is disjoint from the quintasymptotic primes of Φ. Also, by using the generalized Lichtenbaum-Hartshorne vanishing theorem we show that, if (R,) is a d-dimensional local quasi-unmixed ring, then , the dth local cohomology module of R with respect to Φ, vanishes if and only if there...
Orhan Gurgun, Sait Halicioglu and Burcu Ungor (2015)
Communications in Mathematics
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In this paper, we introduce a subclass of strongly clean rings. Let be a ring with identity, be the Jacobson radical of , and let denote the set of all elements of which are nilpotent in . An element is called provided that there exists an idempotent such that and or is an element of . A ring is said to be in case every element in is very -clean. We prove that every very -clean ring is strongly -rad clean and has stable range one. It is shown that for a...
C. Dorsett (1979)
Matematički Vesnik
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Leonid F. Barannyk, Dariusz Klein (2004)
Colloquium Mathematicae
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Let S be a commutative local ring of characteristic p, which is not a field, S* the multiplicative group of S, W a subgroup of S*, G a finite p-group, and a twisted group ring of the group G and of the ring S with a 2-cocycle λ ∈ Z²(G,S*). Denote by the set of isomorphism classes of indecomposable -modules of S-rank m. We exhibit rings for which there exists a function such that and is an infinite set for every natural n > 1. In special cases contains every natural...
M. Mršević (1979)
Matematički Vesnik
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Evgenii L. Bashkirov, Esra Pekönür (2016)
Commentationes Mathematicae Universitatis Carolinae
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Let be an associative and commutative ring with , a subring of such that , an integer. The paper describes subrings of the general linear Lie ring that contain the Lie ring of all traceless matrices over .
Dihua Jiang, Chufeng Nien, Shaun Stevens (2015)
Journal of the European Mathematical Society
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The Local Converse Problem is to determine how the family of the local gamma factors characterizes the isomorphism class of an irreducible admissible generic representation of , with a non-archimedean local field, where runs through all irreducible supercuspidal representations of and runs through positive integers. The Jacquet conjecture asserts that it is enough to take . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet...
Vincent Thilliez (2002)
Studia Mathematica
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In rings of formal power series in several variables whose growth of coefficients is controlled by a suitable sequence (such as rings of Gevrey series), we find precise estimates for quotients F/Φ, where F and Φ are series in such that F is divisible by Φ in the usual ring of all power series. We give first a simple proof of the fact that F/Φ belongs also to , provided is stable under derivation. By a further development of the method, we obtain the main result of the paper,...
Mehdi Parsinia (2016)
Commentationes Mathematicae Universitatis Carolinae
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Let denote a subalgebra of which is closed under local bounded inversion, briefly, an -subalgebra. These subalgebras were first introduced and studied in Redlin L., Watson S., Structure spaces for rings of continuous functions with applications to realcompactifications, Fund. Math. 152 (1997), 151–163. By characterizing maximal ideals of , we generalize the notion of -ideals, which was first introduced in Acharyya S.K., De D., An interesting class of ideals in subalgebras of ...
Stephen Kudla, Michael Rapoport (2014)
Annales de l’institut Fourier
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We show that the Deligne formal model of the Drinfeld -adic half-plane relative to a local field represents a moduli problem of polarized -modules with an action of the ring of integers in a quadratic extension of . The proof proceeds by establishing a comparison isomorphism with the Drinfeld moduli problem. This isomorphism reflects the accidental isomorphism of and for a two-dimensional split hermitian space for .
Kamal Paykan (2017)
Czechoslovak Mathematical Journal
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A ring is called a right -ring if its socle, , is projective. Nicholson and Watters have shown that if is a right -ring, then so are the polynomial ring and power series ring . In this paper, it is proved that, under suitable conditions, if has a (flat) projective socle, then so does the skew inverse power series ring and the skew polynomial ring , where is an associative ring equipped with an automorphism and an -derivation . Our results extend and unify many existing...
Laurent Berger (2014)
Journal de l’École polytechnique — Mathématiques
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Let be a finite extension of . The field of norms of a -adic Lie extension is a local field of characteristic which comes equipped with an action of . When can we lift this action to characteristic , along with a compatible Frobenius map? In this note, we formulate precisely this question, explain its relevance to the theory of -modules, and give a condition for the existence of certain types of lifts.
Ivan Chajda, Filip Švrček (2011)
Discussiones Mathematicae - General Algebra and Applications
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We study unitary rings of characteristic 2 satisfying identity for some natural number p. We characterize several infinite families of these rings which are Boolean, i.e., every element is idempotent. For example, it is in the case if or or for a suitable natural number n. Some other (more general) cases are solved for p expressed in the form or where q is a natural number and .
Marjan Sheibani Abdolyousefi, Neda Pouyan (2024)
Czechoslovak Mathematical Journal
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A ring is feebly nil-clean if for any there exist two orthogonal idempotents and a nilpotent such that . Let be a 2-primal feebly nil-clean ring. We prove that every matrix ring over is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and nilpotent matrices.
Dachun Yang, Sibei Yang
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Let Φ be a concave function on (0,∞) of strictly critical lower type index and (the class of local weights introduced by V. S. Rychkov). We introduce the weighted local Orlicz-Hardy space via the local grand maximal function. Let for all t ∈ (0,∞). We also introduce the BMO-type space and establish the duality between and . Characterizations of , including the atomic characterization, the local vertical and the local nontangential maximal function characterizations, are...