Article overview
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 fieldsDiscrete valuationsRing valuationsLatticesFuzzy setsFuzzy rings$L$-set$L$-subrings.
AMS Subject Classification
13F30, 11T06, 11H06.
Reference information
How to Cite
Roberto Fernandez-Soriano, Pablo Lam-Estrada, P. Siva Kota Reddy (2025). VALUATION RINGS IN FUNCTION FIELDS ONTO LATTICES. South East Asian Journal of Mathematics and Mathematical Sciences, 21(2), 65-80.