On truncations of valuations

2021/04/17 by Novacoski, Josnei Antonio, de Souza, Caio Henrique Silva · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13A18

paper · doi:10.48550/arxiv.2104.08609

Abstract

In this paper we study the truncation ν_q of a valuation ν on a polynomial q. It is known that when q is a key polynomial, then ν_q is a valuation. It is also known that the converse does not hold. We show that when q is a key polynomial, then ν_q is the restriction of the truncation given by an optimizing root of q. We also discuss which conditions assure that ν_q=ν. Finally, we assume that ν_q is a valuation and present some conditions, given in terms of the graded algebra, to assure that q is a key polynomial.

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• On the distances of an element to its conjugates

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