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Relevant bibliographies by topics / Irreducibility criteria

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Academic literature on the topic 'Irreducibility criteria'

Author: Grafiati

Published: 24 April 2022

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Journal articles on the topic "Irreducibility criteria"

1

Churchill, Richard C., and Yang Zhang. "Irreducibility criteria for skew polynomials." Journal of Algebra 322, no. 11 (2009): 3797–822. http://dx.doi.org/10.1016/j.jalgebra.2009.08.012.

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Bellettini, Giovanni, Maurizio Paolini, and Yi-Sheng Wang. "Numerical irreducibility criteria for handlebody links." Topology and its Applications 284 (October 2020): 107361. http://dx.doi.org/10.1016/j.topol.2020.107361.

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3

Bonciocat, Anca Iuliana, Nicolae Ciprian Bonciocat, and Mihai Cipu. "Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 1 (2014): 73–84. http://dx.doi.org/10.2478/auom-2014-0007.

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AbstractWe provide irreducibility criteria for multiplicative convolutions of polynomials with integer coefficients, that is, for polynomials of the form hdeg f · f(g/h), where f, g, h are polynomials with integer coefficients, and g and h are relatively prime. The irreducibility conditions are expressed in terms of the prime factorization of the leading coefficient of the polynomial hdeg f · f(g/h), the degrees of f, g, h, and the absolute values of their coefficients. In particular, by letting h = 1 we obtain irreducibility conditions for compositions of polynomials with integer coefficients.

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Antonio Cafure and Eda Cesaratto. "Irreducibility Criteria for Reciprocal Polynomials and Applications." American Mathematical Monthly 124, no. 1 (2017): 37. http://dx.doi.org/10.4169/amer.math.monthly.124.1.37.

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5

Narita, Hiro-aki, Ameya Pitale, and Ralf Schmidt. "Irreducibility criteria for local and global representations." Proceedings of the American Mathematical Society 141, no. 1 (2012): 55–63. http://dx.doi.org/10.1090/s0002-9939-2012-11438-8.

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6

Bonciocat, N. C. "Irreducibility criteria for compositions of multivariate polynomials." Acta Mathematica Hungarica 156, no. 1 (2018): 172–81. http://dx.doi.org/10.1007/s10474-018-0818-7.

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7

Bonciocat, Anca Iuliana, Nicolae Ciprian Bonciocat, Yann Bugeaud, and Mihai Cipu. "Apollonius circles and irreducibility criteria for polynomials." Indagationes Mathematicae 33, no. 2 (2022): 421–39. http://dx.doi.org/10.1016/j.indag.2021.09.008.

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8

Bonciocat, Nicolae Ciprian, Yann Bugeaud, Mihai Cipu, and Maurice Mignotte. "Some Pólya-Type Irreducibility Criteria for Multivariate Polynomials." Communications in Algebra 40, no. 10 (2012): 3733–44. http://dx.doi.org/10.1080/00927872.2011.594136.

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9

Filaseta, Michael. "Irreducibility Criteria for Polynomials with non-negative Coefficients." Canadian Journal of Mathematics 40, no. 2 (1988): 339–51. http://dx.doi.org/10.4153/cjm-1988-013-6.

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In [7, b.2, VIII, 128] Pólya and Szegö state the following theorem of A. Cohn:THEOREM 1. Let dndn−x … d0 be the decimal representation of a prime. Thenis irreducible.Thus, for example, since 1289 is prime, x3 + 2x2 + 8x + 9 is irreducible. Brillhart, Odlyzko, and the author generalized Cohn's Theorem in three different directions. As examples of these types of generalizations, we note the following results, the first two of which are special cases of a result in [1] and the third of a result in [3].THEOREM 2. Let dndn−x … d0 be the base b representation of a prime where b is an integer ≧2. Thenis irreducible.THEOREM 3. Letbe such that f(10) is prime and 0 ≦ dj ≦ 167 for j = 0, 1, …, n. Then f(x) is irreducible.

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Győry, K., L. Hajdu, and R. Tijdeman. "Irreducibility criteria of Schur-type and Pólya-type." Monatshefte für Mathematik 163, no. 4 (2010): 415–43. http://dx.doi.org/10.1007/s00605-010-0241-9.

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Dissertations / Theses on the topic "Irreducibility criteria"

1

Molev, A. I., and Andreas Cap@esi ac at. "Irreducibility Criterion for Tensor Products of Yangian Evaluation." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi939.ps.

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Books on the topic "Irreducibility criteria"

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Caramello, Olivia. Theories of presheaf type: general criteria. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0008.

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This chapter carries out a systematic investigation of the class of geometric theories of presheaf type (i.e. classified by a presheaf topos), by using in particular the results on flat functors established in Chapter 5. First, it establishes a number of general results on theories of presheaf type, notably including a definability theorem and a characterization of the finitely presentable models of such a theory in terms of formulas satisfying a key property of irreducibility. Then it presents a fully constructive characterization theorem providing necessary and sufficient conditions for a theory to be of presheaf type expressed in terms of the models of the theory in arbitrary Grothendieck toposes. This theorem is shown to admit a number of simpler corollaries which can be effectively applied in practice for testing whether a given theory is of presheaf type as well as for generating new examples of such theories.

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Book chapters on the topic "Irreducibility criteria"

1

Bishnoi, Anuj, and Sudesh K. Khanduja. "Some Extensions and Applications of the Eisenstein Irreducibility Criterion." In Quadratic Forms, Linear Algebraic Groups, and Cohomology. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6211-9_10.

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El Fadil, Lhoussain, and Mohamed Faris. "On the Irreducible Factors of a Polynomial and Applications to Extensions of Absolute Values." In Recent Advances in Polynomials [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.100021.

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Polynomial factorization over a field is very useful in algebraic number theory, in extensions of valuations, etc. For valued field extensions, the determination of irreducible polynomials was the focus of interest of many authors. In 1850, Eisenstein gave one of the most popular criterion to decide on irreducibility of a polynomial over Q. A criterion which was generalized in 1906 by Dumas. In 2008, R. Brown gave what is known to be the most general version of Eisenstein-Schönemann irreducibility criterion. Thanks to MacLane theory, key polynomials play a key role to extend absolute values. In this chapter, we give a sufficient condition on any monic plynomial to be a key polynomial of an absolute value, an irreducibly criterion will be given, and for any simple algebraic extension L=Kα, we give a method to describe all absolute values of L extending ∣∣, where K is a discrete rank one valued field.

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Reports on the topic "Irreducibility criteria"

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Tekir, Ünsal, and Suat Koç. Eisenstein Irreducibility Criterion for Modules. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2021. http://dx.doi.org/10.7546/crabs.2021.01.03.

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