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://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://openscience.fr/Extension-of-Semistar-Operations
IS - Issue 2 (Special CSMT 2022)
VL - 14
ER -