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$1$-Absorbing prime property in lattices | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).، تیر 2026، صفحه 1-14 اصل مقاله (195.93 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.28061.1693 | ||
| نویسنده | ||
| Sh. Ebrahimi Atani* | ||
| Department of Pure Mathematics, University of Guilan, Rasht, Iran | ||
| چکیده | ||
| Let $\pounds$ be a bounded distributive lattice. Following the concept of $1$-absorbing prime ideal, we define $1$-absorbing prime filters of $\pounds$. A proper filter $F$ of $\pounds$ is called $1$-absorbing prime filter of $\pounds$ if whenever non-zero elements $a, b, c \in \pounds$ and $a \vee b \vee c \in F$, then either $a \vee b \in F$ or $c \in F$. We will make an intensive investigate the basic properties and possible structures of these filters. | ||
| کلیدواژهها | ||
| Lattice؛ Filter؛ 1-Absorbing filter | ||
| مراجع | ||
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1] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., (3) 75 (2007), 417-429. [2] G. Birkhoff, Lattice theory, Amer. Math. Soc., 1973. [3] E. M. Bouba, M. Tamekkante, U. Tekir and S. Koc, Notes on 1-absorbing prime ideals, Comptes rendus de PAcademie bulgare des sciences, (5) 75 (2022), 631-639. [4] G. C˘alug˘areanu, Lattice Concepts of Module Theory, Kluwer Academic Publishers, 2000. [5] S. Ebrahimi Atani and M. sedghi Shanbeh Bazari, On 2-absorbing filters of lattices, Discuss. Math. Gen. Algebra Appl., 36 (2016), 157-168. [6] S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel and M. Sedghi Shanbeh Bazari, A simiprime filter-based identity-summand graph of a lattice, Le Matematiche Vol. LXX III (2018) - Fasc. II, 297-318. [7] S. Ebrahimi Atani, On baer filters of bounded distributive lattices, Quasigroups and Related Systems, 32 (2024), 1-20. [8] S. Ebrahimi Atani, The identity-filter graph of lattices, Palestine Journal of Mathematics, (1) 13 (2024), 77-90. [9] S. Ebrahimi Atani, J-filters of bounded lattices, Eur. J. Math. Appl., (4) 12 (2024), DOI:10.28919/ejma.2024.4.12. [10] S. Ebrahimi Atani, G-supplemented property in the lattices, Mathematica Bohemica, (4) 147 (2022), 525-545. [11] A. El Khalfi, M. Issoual, N. Mahdou and A. Reinhart, Commutative rings with oneabsorbing factorization, Commun. Algebra, (6) 49 (2021), 2689-2703. [12] J. Huckaba, Rings with Zero-Divisors, New York/Basil, Marcel Dekker, 1988. [13] A. Yassine, M. J. Nikmehr and R. Nikandish, On 1-absorbing prime ideas of commutative rings, J. Algebra Appl., (10) 20 (2021), 2150175. | ||
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