The $lambda$-super socle of the ring of continuous functions
| Autor: | Simin Mehran, Mehrdad Namdari |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Categories and General Algebraic Structures with Applications, Vol 6, Iss Speical Issue on the Occasion of Banaschewski's 90th Birthday (I), Pp 37-50 (2017) |
| Druh dokumentu: | article |
| ISSN: | 2345-5853 2345-5861 |
| Popis: | 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 $lambdaleq |X|$) 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 $lambda geqaleph_0$. 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 $xin X$. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|