On $F$-Zariski topology in a poset

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Modern Education Societies Nowrosjee Wadia College, Pune-411001, India

2 Department of Mathematics, Fergusson College(Autonomous), Pune-411004, India

Abstract

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 $Spec_F(Q).$

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References

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Transactions on Combinatorics

Articles in Press, Corrected Proof
Available Online from 10 May 2026

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History

  • Receive Date: 11 March 2025
  • Revise Date: 31 December 2025
  • Accept Date: 03 May 2026
  • Published Online: 10 May 2026

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