Abstract:
The purpose of this research paper is threefold: first, to introduce new constructions in the category of real semigroups (RS): locally constant functions on a topological space with values in a RS, directed inductive limits and RS-sums, an analog of a coproduct for RSs. Secondly, to obtain some understanding of the space of RS-characters of an infinite product of RSs and, lastly, to establish the preservation of finite products and arbitrary directed inductive limits by the natural functor from the category of commutative unitary rings into that of RSs. The basic references for real semigroups, whose notation and terminology we adopt, are the papers cited under Dickmann-Petrovich (see References). We are grateful to the referee for the careful reading of the text and the valuable comments and corrections that improved the presentation. © 2017 Amerian Mathematial Soiety.
Registro:
| Documento: |
Artículo
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| Título: | Constructions in the category of real semigroups |
| Autor: | Dickmann, M.; Miraglia, F.; Petrovich, A. |
| Filiación: | Équipe de Logique Mathématique, Institut de Mathématiques de Jussieu − Paris Rive Gauche, Universités de Paris VI et VII, France
Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil
Departamento de Matematicas, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, 1428, Argentina
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| Año: | 2017
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| Volumen: | 697
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| Página de inicio: | 107
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| Página de fin: | 142
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| DOI: |
http://dx.doi.org/10.1090/conm/697/14048 |
| Título revista: | Contemporary Mathematics
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| Título revista abreviado: | Contemp. Math.
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| ISSN: | 02714132
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02714132_v697_n_p107_Dickmann |
Referencias:
- Andradas, C., Bröcker, L., Ruiz, J.M., Constructible sets in real geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) (1996) [Results in Mathematics and Related Areas (3)], 33. , Springer-Verlag, Berlin, MR1393194
- Bochnak, J., Coste, M., Roy, M.-F., Real algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 36. , Springer-Verlag, Berlin, 1998. Translated from the 1987 French original; Revised by the authors. MR1659509
- Dickmann, M.A., Miraglia, F., Special groups: Boolean-theoretic methods in the theory of quadratic forms (2000) Mem. Amer. Math. Soc, 145 (689), p. 247. , With appendixes A and B by Dickmann and A. Petrovich. MR1677935
- Dickmann, M., Miraglia, F., Quadratic form theory over preordered von Neumann-regular rings (2008) J. Algebra, 319 (4), pp. 1696-1732. , MR2383063
- Dickmann, M., Miraglia, F., Representation of reduced special groups in algebras of continuous functions, Quadratic forms—algebra, arithmetic, and geometry (2009) Contemp. Math, 493, pp. 83-97. , Amer. Math. Soc., Providence, RI, MR2537094
- Dickmann, M., Miraglia, F., Tribute Series, 17. , Rings and Real Semigroups, Jean-Yves Béziau and Marcelo Esteban Coniglio (eds.), College Publications, 23-51, London, 2011
- Dickmann, M., Miraglia, F., Faithfully quadratic rings (2015) Mem. Amer. Math. Soc, 238 (1128), p. 123. , MR3402380
- Dickmann, M., Petrovich, A., Real semigroups and abstract real spectra. I, Algebraic and arithmetic theory of quadratic forms (2004) Contemp. Math, 344, pp. 99-119. , Amer. Math. Soc., Providence, RI, MR2058670
- Dickmann, M., Petrovich, A., The three-valued logic of quadratic form theory over real rings (2008) Andrzej Mostowski and Foundational Studies, IOS, pp. 49-67. , Amsterdam, MR2422679
- Dickmann, M., Petrovich, A., Real Semigroups, Real Spectra and Quadratic Forms over Rings, (In Preparation), , http://www.ime.usp.br/˜miraglia/textos/RS-fev-16.pdf
- Dickmann, M., Petrovich, A., Spectral real semigroups (English, with English and French summaries) (2012) Ann. Fac. Sci. Toulouse Math, 21 (6-2), pp. 359-412. , MR2978099
- Dickmann, M., Schwartz, N., Tressl, M., Spectral Spaces, , (to appear in Cambridge University Press)
- Hochster, M., Prime ideal structure in commutative rings (1969) Trans. Amer. Math. Soc, 142, pp. 43-60. , MR0251026
- Hofmann, K.H., Representations of algebras by continuous sections (1972) Bull. Amer. Math. Soc., 78, pp. 291-373. , MR0347915
- Murray, A., (1996) Marshall, Spaces of Orderings and Abstract Real Spectra, Lecture Notes in Mathematics, 1636. , Springer-Verlag, Berlin, MR1438785
- Miraglia, F., (2007) Introduction to Partially Ordered Structures and Sheaves, Polimetrica Scientific Publishers, Contemporary Logic Series 1, , Milan
Citas:
---------- APA ----------
Dickmann, M., Miraglia, F. & Petrovich, A.
(2017)
. Constructions in the category of real semigroups. Contemporary Mathematics, 697, 107-142.
http://dx.doi.org/10.1090/conm/697/14048---------- CHICAGO ----------
Dickmann, M., Miraglia, F., Petrovich, A.
"Constructions in the category of real semigroups"
. Contemporary Mathematics 697
(2017) : 107-142.
http://dx.doi.org/10.1090/conm/697/14048---------- MLA ----------
Dickmann, M., Miraglia, F., Petrovich, A.
"Constructions in the category of real semigroups"
. Contemporary Mathematics, vol. 697, 2017, pp. 107-142.
http://dx.doi.org/10.1090/conm/697/14048---------- VANCOUVER ----------
Dickmann, M., Miraglia, F., Petrovich, A. Constructions in the category of real semigroups. Contemp. Math. 2017;697:107-142.
http://dx.doi.org/10.1090/conm/697/14048
