Results 1 to 10 of about 5,376,358 (214)
Advances in Mathematics, 2016 We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of continuous actions of a topological group.
Olivia Caramello, CARAMELLO, OLIVIA
exaly +5 more sources
Annals of Pure and Applied Logic, 1997 This paper proposes a generalization of Kolchin's Galois theory of differential fields. In the Kolchin theory, the Galois groups correspond to algebraic groups over the subfield of constants; moreover every algebraic group can arise in this way. In this paper, the constants are replaced by an arbitrary differential algebraic set \(X\). Accordingly, \(X\
Anand Pillay
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Noncyclic BCH and Srivastava codes over the subgroup of the groups of units of Galois rings $${G}{R}({{q}}^{{u}},{m})$$ for advanced error control [PDF]
Scientific ReportsThis paper presents a systematic algebraic construction of noncyclic generalizations of BCH and Srivastava codes over Galois rings $$GR\left({q}^{u},m\right).$$ The proposed codes are defined via parity-check matrices whose entries are carefully chosen ...
Muhammad Sajjad +4 more
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Formalizing Galois Theory [PDF]
Experimental Mathematics, 2021 15 ...
Thomas Browning, Patrick Lutz
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Applications of the Projective Space PG (3,8) in Coding Theory [PDF]
مجلة التربية والعلم, 2023 The main objective of this research is to present the relationship between the subject of coding theory and three-dimensional projection space in the eighth field.
Marwa Almstufa, Nada Yahya
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Two New Classes of Codebooks Asymptotically Achieving the Welch Bound
IEEE Access, 2021 Exponential sums over Galois rings have many applications in coding theory, cryptography and algebraic combinatorics. In this article, we employ additive characters and multiplicative characters over Galois rings to present two classes of codebooks, and ...
Shimin Sun, Li Han, Yang Yan, Yao Yao
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Compositio Mathematica, 1999 We formulate and prove necessary and sufficient conditions for the Galois correspondence to hold for the ring of p-adic periods B+dR.
IOVITA, ADRIAN, ZAHARESCU A.
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Galois orbits of TQFTs: symmetries and unitarity
Journal of High Energy Physics, 2022 We study Galois actions on 2+1D topological quantum field theories (TQFTs), characterizing their interplay with theory factorization, gauging, the structure of gapped boundaries and dualities, 0-form symmetries, 1-form symmetries, and 2-groups.
Matthew Buican, Rajath Radhakrishnan
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Sur l'existence du sch\'ema en groupes fondametal [PDF]
Épijournal de Géométrie Algébrique, 2020 Let $S$ be a Dedekind scheme, $X$ a connected $S$-scheme locally of finite type and $x\in X(S)$ a section. The aim of the present paper is to establish the existence of the fundamental group scheme of $X$, when $X$ has reduced fibers or when $X$ is ...
Marco Antei +2 more
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Remarks on abstract Galois theory
Manuscrito, 2011 This paper is a historical companion to a previous one, in which it was studied the so-called abstract Galois theory as formulated by the Portuguese mathematician José Sebastião e Silva (see da Costa, Rodrigues (2007)).
Newton C. A. da Costa, Otávio Bueno
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