Publicado

2022-02-14

C∞ - Rings: an Interplay Between Geometry and Logics

Anillos C∞ - una Interacción entre la Geometría y la Lógica

Palabras clave:

C-rings, Smooth Commutative Algebra, Sheaves and Logics (en)
Anillos C, Álgebra Conmutativa Suave, Haces y Lógica (es)

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Autores/as

  • Jean Cerqueira Berni University of Sao Paulo
  • Hugo Luiz Mariano University of Sao Paulo

In this work we give an overview of some logical and geometric aspects of C-rings, presenting some results concerning its universal algebraic aspects, introducing new results in Smooth Commutative Algebra and presenting some categorial considerations about certain special types of them.

En este trabajo damos una descripción general de algunos aspectos lógicos y geométricos de los anillos C, presentando algunos resultados sobre sus aspectos algebraicos universales, introduciendo nuevos resultados en Álgebra Conmutativa Suave y presentando algunas consideraciones categóricas sobre ciertos tipos especiales de ellos.

Referencias

P. Arndt and H. L. Mariano, The von neumann-regular hull of (preordered) rings and quadratic forms, South American Journal of Logic 2 (2016), no. 2, 201-244.

M. F. Atiyah and I.G. MacDonald, Introduction to commutative algebra, Addison Wesley, 1969.

J. C. Berni, Alguns aspectos algébricos e lógicos dos anéis C (some algebraic and logical apects of C-rings, in english), Universidade de Sao Paulo, 2018.

J. C. Berni, R. Figueiredo, and H. L. Mariano, On the order theory for C-reduced C-rings and applications, (preprint) Arxiv.org (2020), no. 2002.00268, 32 pp.

J. C. Berni and H. L. Mariano, Classifying toposes for some theories of C-rings, South American Journal of Logic 4 (2018), no. 2, 313-350.

J. C. Berni and H. L. Mariano, Topics on smooth commutative algebra, (preprint) Arxiv.org (2019), no. 1904.02725, 111 pp.

J. C. Berni and H. L. Mariano, A universal algebraic survey of C-rings, (preprint) Arxiv.org (2019), no. 1904.02728, 73 pp.

J. C. Berni and H. L. Mariano, Von Neumann regular C-rings and applications, (preprint) Arxiv.org (2019), no. 1905.09617, 72 pp.

D. Borisov and K. Kremnizer, Beyond perturbation 1: de Rham spaces, arxiv 41 (2006), no. 1, 279-287.

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D. Joyce, Algebraic Geometry over C-Rings, Memoirs of the American Mathematical Society, 2019.

M. Kamensky, The model completion of the theory of modules over finitely generated commutative algebras, The Journal of Symbolic Logic 74 (2009), no. 3, 1-2.

R. Lavendhomme, Basic Concepts of Synthetic Differential Geometry, Springer Verlag US, 1996.

S. MacLane and I. Moerdijk, Sheaves in Geometry and Logic - A first introduction to Topos Theory, Springer Verlag, 1992.

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I. Moerdijk and G. Reyes, Rings of smooth functions and their localizations i, Journal of Algebra 99 (1986), no. X, 324-336.

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Cómo citar

APA

Cerqueira Berni, J. & Mariano, H. L. (2022). C∞ - Rings: an Interplay Between Geometry and Logics. Boletín de Matemáticas, 27(2). https://revistas.unal.edu.co/index.php/bolma/article/view/101040

ACM

[1]
Cerqueira Berni, J. y Mariano, H.L. 2022. C∞ - Rings: an Interplay Between Geometry and Logics. Boletín de Matemáticas. 27, 2 (feb. 2022).

ACS

(1)
Cerqueira Berni, J.; Mariano, H. L. C∞ - Rings: an Interplay Between Geometry and Logics. Bol. Matemáticas 2022, 27.

ABNT

CERQUEIRA BERNI, J.; MARIANO, H. L. C∞ - Rings: an Interplay Between Geometry and Logics. Boletín de Matemáticas, [S. l.], v. 27, n. 2, 2022. Disponível em: https://revistas.unal.edu.co/index.php/bolma/article/view/101040. Acesso em: 27 dic. 2025.

Chicago

Cerqueira Berni, Jean, y Hugo Luiz Mariano. 2022. «C∞ - Rings: an Interplay Between Geometry and Logics». Boletín De Matemáticas 27 (2). https://revistas.unal.edu.co/index.php/bolma/article/view/101040.

Harvard

Cerqueira Berni, J. y Mariano, H. L. (2022) «C∞ - Rings: an Interplay Between Geometry and Logics», Boletín de Matemáticas, 27(2). Disponible en: https://revistas.unal.edu.co/index.php/bolma/article/view/101040 (Accedido: 27 diciembre 2025).

IEEE

[1]
J. Cerqueira Berni y H. L. Mariano, «C∞ - Rings: an Interplay Between Geometry and Logics», Bol. Matemáticas, vol. 27, n.º 2, feb. 2022.

MLA

Cerqueira Berni, J., y H. L. Mariano. «C∞ - Rings: an Interplay Between Geometry and Logics». Boletín de Matemáticas, vol. 27, n.º 2, febrero de 2022, https://revistas.unal.edu.co/index.php/bolma/article/view/101040.

Turabian

Cerqueira Berni, Jean, y Hugo Luiz Mariano. «C∞ - Rings: an Interplay Between Geometry and Logics». Boletín de Matemáticas 27, no. 2 (febrero 14, 2022). Accedido diciembre 27, 2025. https://revistas.unal.edu.co/index.php/bolma/article/view/101040.

Vancouver

1.
Cerqueira Berni J, Mariano HL. C∞ - Rings: an Interplay Between Geometry and Logics. Bol. Matemáticas [Internet]. 14 de febrero de 2022 [citado 27 de diciembre de 2025];27(2). Disponible en: https://revistas.unal.edu.co/index.php/bolma/article/view/101040

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