On $F$-Zariski topology in a poset

Mundlik, Nilesh; Kshirsagar, Mayur B

doi:10.22108/toc.2026.144609.2255

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	On $F$-Zariski topology in a poset
Transactions on Combinatorics
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 20 اردیبهشت 1405 اصل مقاله (489.4 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2026.144609.2255
نویسندگان
Nilesh Mundlik¹؛ Mayur B Kshirsagar^* ²
¹Department of Mathematics, Modern Education Societies Nowrosjee Wadia College, Pune-411001, India
²Department of Mathematics, Fergusson College(Autonomous), Pune-411004, India
چکیده
Let $Q$ be a partially ordered set, and let F be an $\ell$-filter in $Q.$ An ideal $P$ in a poset $Q$ with ${\color{red}{P}} \cap F=\emptyset $ is called $F$-prime, if there exists a fixed element $f \in F$ such that whenever $(a,b)^\ell \subseteq P,$ for some $a,b \in Q$ then $(f,a)^\ell \subseteq P$ or $(f,b)^\ell \subseteq P.$ In this paper, we study a topology on the set $Spec_F(Q)$ of all $F$-prime ideals in $Q,$ which is a generalization of the prime spectrum $Spec(Q)$ of a poset $Q.$ We also investigate the relationship between order theoretic properties of $Q$ and topological properties of $Spec_F(Q).$
کلیدواژه‌ها
Prime ideal؛ $F$-prime ideal؛ maximal prime ideal

مراجع
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On $F$-Zariski topology in a poset