VALUATION RINGS IN FUNCTION FIELDS ONTO LATTICES

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads :

Volume : 21 , Issue : 2
DOI: https://doi.org/10.56827/SEAJMMS.2025.2102.5
Author :
Roberto Fernandez-Soriano (Escuela Superior de Fisica y Matematicas, Departamento de Matematicas, Instituto Politecnico Nacional (Unidad Zacatenco), CDMX, MEXICO)
Pablo Lam-Estrada (Escuela Superior de Fisica y Matematicas, Departamento de Matematicas, Instituto Politecnico Nacional (Unidad Zacatenco), CDMX, MEXICO)
P. Siva Kota Reddy (*Department of Mathematics,\ JSS Science and Technology University,\ Mysuru - 570006, INDIA)

Abstract

Taking a complete Heyting algebra $L$ and using $L$-sets, we will build the $L$-subrings of valuation and $L$-valuations of an algebraic function field of one variable $F/K$, as a generalization of the valuation rings and discrete valuations of $F/K$, and we will obtain many properties of them, and their analogues to the Theorem of Approximation of an amount finite of non-equivalent valuations.

Keywords and Phrases

Function fields, Discrete valuations, Ring valuations, Lattices, Fuzzy sets, Fuzzy rings, $L$-set, $L$-subrings.

A.M.S. subject classification

13F30, 11T06, 11H06.

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