On weakly $S$-$2$-absorbing filters in lattices
DOI:
https://doi.org/10.13069/jacodesmath.v12i3.318Keywords:
Lattice, Filter, Weakly absorbing filterAbstract
Let \(£\) be a bounded distributive lattice and $S$ a join closed subset of \(£\). Following the concept of weakly $S$-$2$-absorbing submodules, we define weakly $S$-$2$-absorbing filters of \(£\). We will make an intensive investigate the basic properties and possible structures of these filters.
Accepted: 5 July 2024
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References
D. D. Anderson, E. Smith, Weakly prime ideals, Houston J. Math. 29(4) (2003) 831–840.
F. A. A. Almahdi, E. M. Bouba, M. Tamekkante, On weakly (S)-prime ideals of commutative rings, An. St. Univ. Ovidius Constanta 29(2) (2021) 173–186.
G. Birkhoff, Lattice theory, Amer. Math. Soc. (1973).
A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75(3) (2007) 417–429.
G. Călugăreanu, Lattice concepts of module theory, Kluwer Academic Publishers (2000).
S. Ebrahimi Atani, M. Sedghi Shanbeh Bazari, On 2-absorbing filters of lattices, Discuss. Math. Gen. Algebra Appl. 36 (2016) 157–168.
S. Ebrahimi Atani, F. Farzalipour, On weakly primary ideals, Georgian Math. J. 12 (2005) 423–429.
S. Ebrahimi Atani, (G)-Supplemented property in the lattices, Mathematica Bohemica 147(4) (2022) 525–545.
S. Ebrahimi Atani, F. Farzalipour, On weakly prime submodules, Tamkang J. Math. 38 (2007) 247–252.
S. Ebrahimi Atani, Note on weakly 1-absorbing prime filters, Bull. Int. Math. Virtual Inst. 13(3) (2023) 465–478.
S. Ebrahimi Atani, (S)-prime property in lattices, Mathematica 66/89(2) (2024) 168–187.
A. Hamed, A. Malek, (S)-prime ideals of a commutative ring, Beitr. Algebra Geom. (2020) 533–542.
O. A. Naji, On (S)-2-absorbing primary submodules, Filomat 35(5) (2021) 1477–1487.
E. S. Sevim, T. Arabacı, Ü. Tekir, S. Koç, On (S)-prime submodules, Turk. J. Math. 43(2) (2019) 1036–1046.
G. Ulucak, Ü. Tekir, S. Koç, On (S)-2-absorbing submodules and vn-regular modules, An. St. Univ. Ovidius Constanta 28(2) (2020) 239–257.
G. N. Sudharshana, On weakly (S)-2-absorbing submodules, Int. J. Anal. Appl. (2023) 48.
