Publicado
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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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.
E. J. Dubuc, Sur les modèles de la géométrie differentielle synthétique, Cahiers de Topologie et Géométrie Differentielle Catégoriques 20 (1979), no. 3, 231-279.
A. Grothendieck and J. Dieudonné, Élements de Géométrie Algebrique, nst. Hautes Et. Sc., publ. math. nOS, 1960-1967.
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.
M. Makkai and G. Reyes, First Order Categorical Logic: Model-Theoretical Methods in the Theory of Topoi and Related Categories, Springer-Verlag, 1977.
I. Moerdijk and G. Reyes, Rings of smooth functions and their localizations i, Journal of Algebra 99 (1986), no. X, 324-336.
I. Moerdijk, G. Reyes, and N. V. Qu^e, Rings of smooth functions and their localizations ii, Mathematical Logic and Theoretical Computer Science 106 (1987), no. X, 277-300.
R. O. Robson, Model theory and spectra, ournal of Pure and Applied Algebra 106 (1990), no. X, 301-327.
C. Scheiderer, Real and Étale Cohomology, Springer Verlag, 1994.



