TY  - Type of reference 
TI  - Extension of Semistar Operations 
AU  - Gmiza Wafa 
AU  - Hizem Sana 
AB  - 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. 
DO  - 10.21494/ISTE.OP.2023.0934 
JF  - Advances in Pure and Applied Mathematics 
KW  - Semistar operation,  localizing system,  extension of rings,  Zarsiski Topology, Semistar operation,  localizing system,  extension of rings,  Zarsiski Topology,  
L1  - https://www.openscience.fr/IMG/pdf/iste_apam23v14nspe_1.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2023/03/8 
SN  - 1869-6090 
TT  - Extension des operations semistar 
UR  - https://www.openscience.fr/Extension-of-Semistar-Operations 
IS  - Issue 2 (Special CSMT 2022) 
VL  - 14 
ER  -