@ARTICLE{10.21494/ISTE.OP.2023.0934, 

TITLE={Extension of Semistar Operations}, 
  
AUTHOR={Gmiza Wafa, Hizem Sana, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={14}, 

NUMBER={Issue 2 (Special CSMT 2022)}, 
	
YEAR={2023}, 

URL={https://openscience.fr/Extension-of-Semistar-Operations}, 
	
DOI={10.21494/ISTE.OP.2023.0934}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={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.}}