Titre : Extension of Semistar Operations
Auteurs : Gmiza Wafa, Hizem Sana,
Revue : Advances in Pure and Applied Mathematics
Numéro : Issue 2 (Special CSMT 2022)
Volume : 14
Date : 2023/03/8
DOI : 10.21494/ISTE.OP.2023.0934
ISSN : 1869-6090
Résumé : Let R ⊂ T be an extension of integral domains and ∗ be a semistar operation stable of finite type on R. We define a semistar operation ∗1 on T in the following way: for each nonzero T-submodule E of the quotient field K1 of T, let E∗1 = ∪ {E :K1 JT | J ∈ $$$\mathcal{F}$$$∗}, where K1 denotes the quotient field of T and $$$\mathcal{F}$$$∗ the localizing system associated to ∗. In this paper we investigate the basic properties of ∗1. Moreover, we show that the map $$$\varphi$$$ which associates to a semistar operation ∗ stable and of finite type on R, the semistar operation ∗1 is continuous. Furthermore, we give sufficient conditions for $$$\varphi$$$ to be a homeomorphism.
Éditeur : ISTE OpenScience