Abstract
Bu çalışmada eşsonlu (zayıf) g-tümlenmiş kafesler tanımlandı ve bu kafeslerin bazı özellikleri incelendi. Eşsonlu (zayıf) g-tümlenmiş kafeslerin bölüm alt kafeslerinin de eşsonlu (zayıf) g-tümlenmiş olduğu gösterildi. Herhangi sayıda eşsonlu (zayıf) g-tümlenmiş kafeslerin supremumu da eşsonlu (zayıf) g-tümlenmiştir. Kompakt üretilmiş kafeslerde eşsonlu elemanların zayıf g-tümleyenlerinin kompakt elemanlar olarak kabul edilebileceği kanıtlandı. Bu özelliğin kompakt üretilmiş olmayan kafesler için doğru olmadığına bir örnek verildi. Eşsonlu zayıf g-tümlenmiş kompakt üretilmiş kafeslerin eşsonlu g-tümlenmiş olması için gerekli bir koşul verildi.
References
- [1] R. Alizade and S. E. Toksoy, “Cofinitely weak supplemented lattices,” Indian J. Pure Appl. Math., vol. 40, no. 5, pp. 337-346, 2009.
- [2] R. Alizade and S. E. Toksoy, “Cofinitely supplemented modular lattices,” Arab J Sci Eng, vol. 36, no. 6, pp. 919–923, 2011.
- [3] G. Calugareanu, Lattice Concepts of Module Theory. Kluwer Academic Publishers, 2000.
- [4] M. L. Galvao and P. F. Smith, “Chain conditions in modular lattices,” Coll. Math., vol. 76, no. 1, pp. 85–98, 1998.
- [5] B. Koşar, “Cofinitely G-supplemented modules,” British Journal of Mathematics Computer Science, vol. 17, no. 4, pp. 1–6, 2016.
- [6] B. Koşar, C. Nebiyev and A. Pekin, “A generalization of g-supplemented modules,” Miskolc Math. Notes, vol. 20, no. 1, pp. 345–352, 2019.
- [7] C. Nebiyev and H. H. Ökten, “Weakly g-supplemented modules,” Europian J. of Pure and Appl. Math., vol. 10, no. 3, pp. 521–528, 2017.
- [8] H. H. Ökten, “G-supplemented lattices,” Miskolc Math. Notes, vol. 22, no. 1, pp. 435–441, 2021.
- [9] B. Stenström, “Radicals and socles of lattices,” Arch. Math., vol. XX, pp. 258–261, 1969.
- [10] A. Walendziak, “On characterizations of atomistic lattices,” Algebra Univers, vol. 43, no. 1, pp. 31–39, 2009.
Abstract
In this work, cofinitely (weak) g-supplemented lattices are defined and some properties of these lattices are investigated. It is shown that quotient sublattices of cofinitely (weak) g-supplemented lattices are cofinitely (weak) g-supplemented. If 〖{a_i/0} 〗_(i∈I) is a collection of cofinitely (weak) g-supplemented sublattices of L and 1=⋁_(i∈I) a_i, then L is also cofinitely (weak) g-supplemented. It is proved that without loss of generality weak g-supplements of cofinite elements in compactly generated lattices are compact. An example showing that this is not true for lattices which are not cofinitely generated is given. A condition is given under which a compactly generated cofinitely weak g-supplemented lattice is cofinitely g-supplemented.
References
- [1] R. Alizade and S. E. Toksoy, “Cofinitely weak supplemented lattices,” Indian J. Pure Appl. Math., vol. 40, no. 5, pp. 337-346, 2009.
- [2] R. Alizade and S. E. Toksoy, “Cofinitely supplemented modular lattices,” Arab J Sci Eng, vol. 36, no. 6, pp. 919–923, 2011.
- [3] G. Calugareanu, Lattice Concepts of Module Theory. Kluwer Academic Publishers, 2000.
- [4] M. L. Galvao and P. F. Smith, “Chain conditions in modular lattices,” Coll. Math., vol. 76, no. 1, pp. 85–98, 1998.
- [5] B. Koşar, “Cofinitely G-supplemented modules,” British Journal of Mathematics Computer Science, vol. 17, no. 4, pp. 1–6, 2016.
- [6] B. Koşar, C. Nebiyev and A. Pekin, “A generalization of g-supplemented modules,” Miskolc Math. Notes, vol. 20, no. 1, pp. 345–352, 2019.
- [7] C. Nebiyev and H. H. Ökten, “Weakly g-supplemented modules,” Europian J. of Pure and Appl. Math., vol. 10, no. 3, pp. 521–528, 2017.
- [8] H. H. Ökten, “G-supplemented lattices,” Miskolc Math. Notes, vol. 22, no. 1, pp. 435–441, 2021.
- [9] B. Stenström, “Radicals and socles of lattices,” Arch. Math., vol. XX, pp. 258–261, 1969.
- [10] A. Walendziak, “On characterizations of atomistic lattices,” Algebra Univers, vol. 43, no. 1, pp. 31–39, 2009.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | January 31, 2022 |
| Published in Issue | Year 2022 |