TY - JOUR
ID - 33814
TI - The $\lambda$-super socle of the ring of continuous functions
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Mehran, Simin
AU - Namdari, Mehrdad
AD - Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
Y1 - 2017
PY - 2017
VL - 6
IS - Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)
SP - 37
EP - 50
KW - $\lambda$-super socle
KW - $\lambda$-isolated point
KW - one point $\lambda$-compactification
KW - $p_\lambda$-space
DO -
N2 - The concept of $\lambda$-super socle of $C(X)$, denoted by $S_\lambda(X)$ (i.e., the set of elements of $C(X)$ such that the cardinality of their cozerosets are less than $\lambda$, where $\lambda$ is a regular cardinal number with $\lambda\leq |X|$) is introduced and studied. Using this concept we extend some of the basic results concerning $SC_F(X)$, the super socle of $C(X)$ to $S_\lambda(X)$, where $\lambda \geq\aleph_0$. In particular, we determine spaces $X$ for which $SC_F(X)$ and $S_\lambda(X)$ coincide. The one-point $\lambda$-compactification of a discrete space is algebraically characterized via the concept of $\lambda$-super socle. In fact we show that $X$ is the one-point $\lambda$-compactification of a discrete space $Y$ if and only if $S_\lambda(X)$ is a regular ideal and $S_\lambda(X)=O_x$, for some $x\in X$.
UR - https://cgasa.sbu.ac.ir/article_33814.html
L1 - https://cgasa.sbu.ac.ir/article_33814_ae287573db032d67df112083dcb83c8f.pdf
ER -