DIVISOR TOPOLOGIES AND THEIR ENUMERATION | ||
| Journal of Algebraic Systems | ||
| دوره 10، شماره 1، آذر 2022، صفحه 111-119 اصل مقاله (156.7 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2021.9712.1473 | ||
| نویسندگان | ||
| F. Esmaeeli1؛ K. Mirzavaziri2؛ M. Mirzavaziri* 1 | ||
| 1Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran. | ||
| 2Department of Computer Science, School of Mathematics, Statistics and Computer Science, University of Tehran, P.O. Box 141556619, Tehran, Iran. | ||
| چکیده | ||
| For a positive integer $m$, a subset of divisors of $m$ is called a \textit{divisor topology on $m$} if it contains $1 $ and $m$ and it is closed under taking $\gcd$ and $\rm lcm$. If $m=p_1\dots p_n$ is a square free positive integer, then a divisor topology $m$ corresponds to a topology on the set $[n]=\{1,2,\ldots,n\}$. Giving some facts about divisor topologies, we give a recursive formula for the number of divisor topologies on a positive integer. | ||
| کلیدواژهها | ||
| Topology؛ Divisor topology؛ Semi-divisor topology | ||
| مراجع | ||
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