Mathematica Bohemica, first online, pp. 1-21


$G$-supplemented property in the lattices

Shahabaddin Ebrahimi Atani

Received 13 July, 2020.   Published online January 26, 2022.

Abstract:  Let $L$ be a lattice with the greatest element 1. Following the concept of generalized small subfilter, we define $g$-supplemented filters and investigate the basic properties and possible structures of these filters.
Keywords:  filter; $g$-small; $g$-supplemented; lattice
Classification MSC:  06C05; 06C15
DOI:  10.21136/MB.2022.0124-20

PDF available at:  Institute of Mathematics CAS

References:
[1] G. Birkhoff: Lattice Theory. Colloquium Publications 25. AMS, Providence (1967). DOI 10.1090/coll/025 | MR 0227053 | Zbl 0153.02501
[2] G. Călugăreanu: Lattice Concepts of Module Theory. Kluwer Texts in the Mathematical Sciences 22. Kluwer Academic Publishers, Dordrecht (2000). DOI 10.1007/978-94-015-9588-9 | MR 1782739 | Zbl 0959.06001
[3] J. Clark, C. Lomp, N. Vanaja, R. Wisbauer: Lifting Modules: Supplements and Projectivity in Module Theory. Frontiers in Mathematics. Birkhäuser, Basel (2006). DOI 10.1007/3-7643-7573-6 | MR 2253001 | Zbl 1102.16001
[4] S. Ebrahimi Atani, M. Chenari: Supplemented property in the lattices. Serdica Math. J. 46 (2020), 73-88. MR 4124062
[5] S. Ebrahimi Atani, S. Dolati Pish Hesari, M. Khoramdel, M. Sedghi Shanbeh Bazari: A semiprime filter-based identity-summand graph of a lattice. Matematiche 73 (2018), 297-318. DOI 10.4418/2018.73.2.5 | MR 3884546 | Zbl 07142702
[6] S. Ebrahimi Atani, M. Sedghi Shanbeh Bazari: On 2-absorbing filters of lattices. Discuss. Math., Gen. Algebra Appl. 36 (2016), 157-168. DOI 10.7151/dmgaa.1253 | MR 3594959 | Zbl 07278179
[7] F. Kasch, E. A. Mares: Eine Kennzeichnung semi-perfekter Moduln. Nagoya Math. J. 27 (1966), 525-529. DOI 10.1017/S0027763000026350 | MR 0199227 | Zbl 0158.28901
[8] B. Koşar, C. Nebiyev, N. Sökmez: $g$-supplemented modules. Ukr. Math. J. 67 (2015), 975-980. DOI 10.1007/s11253-015-1127-8 | MR 3432491 | Zbl 1352.16001
[9] S. H. Mohamed, B. J. Müller: Continuous and Discrete Modules. London Mathematical Society Lecture Note Series 147. Cambridge University Press, London (1990). DOI 10.1017/CBO9780511600692 | MR 1084376 | Zbl 0701.16001
[10] T. C. Quynh, P. H. Tin: Some properties of $e$-supplemented and $e$-lifting modules. Vietnam J. Math. 41 (2013), 303-312. DOI 10.1007/s10013-013-0022-6 | MR 3103264 | Zbl 1281.16006
[11] R. Wisbauer: Foundations of Module and Ring Theory: A Handbook for Study and Research. Algebra, Logic and Applications 3. Gordon and Breach, Philadelphia (1991). MR 1144522 | Zbl 0746.16001
[12] D. X. Zhou, X. R. Zhang: Small-essential submodules and Morita duality. Southeast Asian Bull. Math. 35 (2011), 1051-1062. MR 2907772 | Zbl 1265.16011
[13] H. Zöschinger: Komplementierte Moduln über Dedekindringen. J. Algebra 29 (1974), 42-56 (In German.). DOI 10.1016/0021-8693(74)90109-4 | MR 0340347 | Zbl 0277.13008

Affiliations:   Shahabaddin Ebrahimi Atani, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran, e-mail: ebrahimi@guilan.ac.ir


 
PDF available at: