7 citations · 13 across the 11 of their papers we have counts for
14 papers
Real radiciality and monoreal extensions
Goulwen Fichou, Jean-Philippe Monnier, Ronan Quarez
We study irreducible polynomials admitting a single real root in any real closed field extension of the base field, called monoreal polynomials. We show some stability properties s…
On central orderings
Goulwen Fichou, Jean-Philippe Monnier, Ronan Quarez
We define the notion of central orderings for a general commutative ring which generalizes the notion of central points of irreducible real algebraic varieties. We study a cent…
Algebraic characterizations of homeomorphisms between algebraic varieties
François Bernard, Goulwen Fichou, Jean-Philippe Monnier +1
We address the question of finding algebraic properties that are respectively equivalent, for a morphism between algebraic varieties over an algebraically closed field of character…
Central Algebraic Geometry and Seminormality
Jean-Philippe Monnier
We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to th…
Integral Closures In Real Algebraic Geometry
Jean-Philippe Monnier, Goulwen Fichou, Ronan Quarez
We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous ratio…
Substitution Property for the Ring of Continuous Rational Functions
Goulwen Fichou, Jean-Philippe Monnier, Ronan Quarez
We study the substitution property for the ring R 0 (V) of continuous rational functions on a real algebraic affine variety V. We show that R 0 (V) satisfies a substitution propert…