TY - JOUR
AU - Ghasemzadeh, S.
AU - Namdari, M.
PY - 2019/04/01
Y2 - 2022/11/29
TI - When is the super socle of C(X) prime?
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 20
IS - 1
SE -
DO - 10.4995/agt.2019.10731
UR - https://polipapers.upv.es/index.php/AGT/article/view/10731
SP - 231-236
AB - <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>
ER -