On the irreducibility of slice algebraic sets

2025/07/29 by Gori, Anna, Sarfatti, Giulia, Vlacci, Fabio
#16S36 #30G35 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.21674

Abstract

In the present paper we investigate the relations between irreducible slice algebraic sets in ℍⁿ and quasi prime right ideals of the ring of slice regular polynomials in n quaternionic variables. We provide algebraic conditions on right ideals of slice regular polynomials which guarantee the irreducibility of the corresponding slice algebraic sets and show that radical ideals associated with irreducible slice algebraic sets are quasi prime. Furthermore we establish that this correspondence is an equivalence in the case of principal right ideals.

Citations

• A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables
• On the geometry of zero sets of central quaternionic polynomials
• Zero sets and Nullstellensatz type theorems for slice regular quaternionic polynomials

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• On ideals in quantales -- I
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