@article{Ghasemzadeh_Namdari_2019, title={When is the super socle of C(X) prime?}, volume={20}, url={https://polipapers.upv.es/index.php/AGT/article/view/10731}, DOI={10.4995/agt.2019.10731}, abstractNote={<p>Let SC<sub>F</sub>(X) denote the ideal of C(X) consisting of functions which are zero everywhere except on a countable number of points of X. It is generalization of the socle of C(X) denoted by C<sub>F</sub>(X). Using this concept we extend some of the basic results concerning C<sub>F</sub>(X) to SC<sub>F</sub>(X). In particular, we characterize the spaces X such that SC<sub>F</sub>(X) is a prime ideal in C(X) (note, C<sub>F</sub>(X) is never a prime ideal in C(X)). This may be considered as an advantage of SC<sub>F</sub>(X) over C(X). We are also interested in characterizing topological spaces X such that C<sub>c</sub>(X) =R+SC<sub>F</sub>(X), where C<sub>c</sub>(X) denotes the subring of C(X) consisting of functions with countable image.</p>}, number={1}, journal={Applied General Topology}, author={Ghasemzadeh, S. and Namdari, M.}, year={2019}, month={Apr.}, pages={231–236} }