RAD- ® -SUPPLEMENTED LATTICES

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Bicer C. I. G. D. E. M., Nebiyev C. E. L. I. L.

MISKOLC MATHEMATICAL NOTES, vol.24, no.2, pp.665-671, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.18514/mmn.2023.4030
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.665-671
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this work, we define Rad- & REG; -supplemented and strongly Rad- & REG; -supplemented lattices and give some properties of these lattices. We generalize some properties of Rad- & REG; -supplemented modules to lattices. Let L be a lattice and 1= a1 & REG;a2 & REG; ... & REG;an with a1, a2, ... , an E L. If ai/0 is Rad- & REG; - supplemented for every i = 1, 2, ... , n, then L is also Rad- & REG; - supple-mented. Let L be a distributive Rad-& REG;-supplemented lattice. Then 1/u is Rad-& REG;-supplemented for every u E L. We also define completely Rad- & REG; -supplemented lattices and prove that every Rad- & REG; -supplemented lattice with SSP property is completely Rad- & REG; - supplemented.