The $\lambda$-super socle of the ring of continuous functions | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 6، دوره 6، Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)، فروردین 2017، صفحه 37-50 اصل مقاله (464.44 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Simin Mehran؛ Mehrdad Namdari | ||
| Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. | ||
| چکیده | ||
| 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 $x\in X$. | ||
تازه های تحقیق | ||
Dedicated to Bernhard Banaschewski on the occasion of his 90th birthday | ||
| کلیدواژهها | ||
| $\lambda$-super socle؛ $\lambda$-isolated point؛ one point $\lambda$-compactification؛ $p_\lambda$-space | ||
| مراجع | ||
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