On $F$-Zariski topology in a poset

Mundlik, Nilesh; Kshirsagar, Mayur B

doi:10.22108/toc.2026.144609.2255

تعداد نشریات	44
تعداد شماره‌ها	1,891
تعداد مقالات	15,352
تعداد مشاهده مقاله	44,706,131
تعداد دریافت فایل اصل مقاله	17,968,468

	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 (489.5 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
[1] J. Abuhlail, A Zariski topology for modules, Commun. Algebra, 39 no. 11 (2011) 4163–4182. [2] M. F. Atiyah and I. G. MacDonald, Introduction to commutative algebra, Addison-Wesley, Reading, MA, 1969. [3] F. Callialp, G. Ulucak and ¨U. Tekir, On Zariski topology over an L-module M, Turk. J. Math., 41 no. 2 (2017) 326–336. [4] I. Chajda, Complemented ordered sets, Arch. Math. (Brno), 28 no. 1-2 (1992) 25–34. [5] W. Fulton, An introduction to algebraic geometry, Addison-Wesley, 2008. [6] V. A. Gorbunov and V. I. Tumanov, On the existence of prime ideals in semi-distributive lattices, Algebra Univers., 16 no. 2 (1983) 250–252. [7] G. Gr¨atzer, General lattice theory, Birkh¨auser, 1998. [8] V. Joshi and N. Mundlik, Prime ideals in 0-distributive posets, Cent. Eur. J. Math., 11 no. 5 (2013) 940–955. [9] V. Joshi and N. Mundlik, Prime ideals in zero distributive posets, Asain-Eur. J. Math., 5 no. 3 (2012) 1–9. [10] C. Kim, The Zariski topology on the prime spectrum of a commutative ring, Doctoral dissertation, California State University, Northridge, (2018). [11] J. Larmerov´a and J. Rachunek, Translations of distributive and modular ordered sets, Acta. Univ. Palack. Olomuc. Fac. Rerum. Nature. Math., 91 (1988) 13–23. [12] N. Mundlik, V. Joshi and R. Halaˇs, The hull-kernel topology on prime ideals in posets, Soft Comput., 21 no. 7 (2017) 1653–1655. [13] J. Munkres, Topology: A first course, 23, Englewood Cliffs, NJ: Prentice-Hall, 1975. [14] E. Sevim, T. Arabaci, ¨U. Tekir and S. Koc, On S-prime submodules, Turk. J. Math., 43 no. 2 (2019) 1036–1046. [15] A. Toroghy and H. Farshadifar, The Zariski topology on second spectrum of a module, Algebra Colloq., 21 no. 04 (2019) 671–688. [16] P. V. Venkatanarasimhan, Semi-ideals in posets, Math. Ann.,185 (1970) 338–348. [17] E. Yildiz, B. Ersoy, ¨U. Tekir and S. Koc, On S-Zariski topology, Communication in Algebra, 49 no. 3 (2021) 1212–1224.
آمار تعداد مشاهده مقاله: 70 تعداد دریافت فایل اصل مقاله: 104

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

On $F$-Zariski topology in a poset