@article {
author = {Mehran, Simin and Namdari, Mehrdad},
title = {The $\lambda$-super socle of the ring of continuous functions},
journal = {Categories and General Algebraic Structures with Applications},
volume = {6},
number = {Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)},
pages = {37-50},
year = {2017},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {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 $x\in X$.},
keywords = {$\lambda$-super socle,$\lambda$-isolated point,one point $\lambda$-compactification,$p_\lambda$-space},
url = {https://cgasa.sbu.ac.ir/article_33814.html},
eprint = {https://cgasa.sbu.ac.ir/article_33814_ae287573db032d67df112083dcb83c8f.pdf}
}