共查询到20条相似文献,搜索用时 31 毫秒
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Anuj Jakhar Sudesh K. Khanduja Neeraj Sangwan 《Journal of Pure and Applied Algebra》2018,222(4):889-899
Let v be a Krull valuation of a field with valuation ring . Let θ be a root of an irreducible trinomial belonging to . In this paper, we give necessary and sufficient conditions involving only for to be integrally closed. In the particular case when v is the p-adic valuation of the field of rational numbers, and , then it is shown that these conditions lead to the characterization of primes which divide the index of the subgroup in , where is the ring of algebraic integers of K. As an application, it is deduced that for any algebraic number field K and any quadratic field L not contained in K, we have if and only if the discriminants of K and L are coprime. 相似文献
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In this paper, we present several necessary conditions for the reversed Dickson polynomial of the second kind to be a permutation of . In particular, we give explicit evaluation of the sum . 相似文献
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《International Journal of Approximate Reasoning》2014,55(9):1830-1842
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Let p be a prime and let be a primitive p-th root of unity. For a finite extension k of containing , we consider a Kummer extension of degree p. In this paper, we show that if and the class number of k is one, the index of is one. We also show that if is tamely ramified with a normal integral basis, the index is at most a power of p. In the last section, we show that there exist infinitely many cubic Kummer extensions of for both wildly and tamely ramified cases, whose integer rings do not have a power integral basis over that of . 相似文献
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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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Cristhian E. Hidber Miguel A. Xicoténcatl 《Journal of Pure and Applied Algebra》2018,222(6):1478-1488
The purpose of this article is to compute the mod 2 cohomology of , the mapping class group of the Klein bottle with q marked points. We provide a concrete construction of Eilenberg–MacLane spaces and fiber bundles , where denotes the configuration space of unordered q-tuples of distinct points in and is the classifying space of the group . Moreover, we show the mod 2 Serre spectral sequence of the bundle above collapses. 相似文献
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Tathagata Basak 《Journal of Pure and Applied Algebra》2018,222(10):3036-3042
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Conditionally on the ABC conjecture, we apply work of Granville to show that a hyperelliptic curve of genus at least three has infinitely many quadratic twists that violate the Hasse Principle iff it has no -rational hyperelliptic branch points. 相似文献
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