Topological closure of ideals of commutative formal power series and applications

par Adya Musson-Leymarie

jeudi 6 juin 2024, 11:00 → 11:30 Europe/Paris

XR 203 (XLIM)

Motivated by applications to the new theory of topological rewriting and especially in the context of rewriting on formal power series, one is bound to ask themselves about the topological properties of the objects involved; for instance, algebraic ideals in the ring of the formal power series. From a general result of Zariski and Samuel, it is known that ideals of commutative formal power series are topologically closed for the I-adic topology induced by the ideal generated by the indeterminates. By means of rewriting methods using standard bases (analogous to Gröbner bases), we present in that talk a constructive proof of this property. Finally, we mention the implications this result has in the equivalence of different confluence properties and in the characterisations of standard bases.