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Journals / Düzce Üniversitesi Bilim ve Teknoloji Dergisi / 2022 / Cilt: 10 - Sayı: 1

Cofinitely (Weak) G-Supplemented Lattices

Eşsonlu (Zayıf) G-Tümlenmiş Kafesler

Sultan Eylem TOKSOY
Pages
476–482
Publication Date
2022-10-12
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A condition is given under which a compactly generated cofinitely weak g-supplemented lattice is cofinitely g-supplemented.

📌 3 Key Takeaways

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Objective & Hypothesis:In this work, cofinitely (weak) g-supplemented lattices are defined and some properties of these lattices are investigated.
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Key Findings & Data: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.
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Conclusion & Impact:A condition is given under which a compactly generated cofinitely weak g-supplemented lattice is cofinitely g-supplemented.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Modüler kafes · g-küçük elemanlar · g-tümlenmiş kafesler

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.

Özet

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.

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Cite This Article

TOKSOY, S. E. (2022). Cofinitely (Weak) G-Supplemented Lattices. Düzce Üniversitesi Bilim ve Teknoloji Dergisi, Cilt: 10 - Sayı: 1, 476–482. https://ajindex.com/articles/493861

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References (10)

  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.