ESSENTIAL SUPPLEMENTED LATTICES

Okten H. H., PEKİN A.

MISKOLC MATHEMATICAL NOTES, vol.21, no.2, pp.1013-1018, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.18514/mmn.2020.3246
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.1013-1018
  • Istanbul University Affiliated: Yes

Abstract

Let L be a complete modular lattice. If every essential element of L has a supplement in L, then L is called an essential supplemented (or briefly e-supplemented) lattice. In this work some properties of these lattices are investigated. Let L be a complete modular lattice and 1 = a(1)Va(2)V...Va(n) with a(i) is an element of L(1 <= i <= n). If ai/0 is e-supplemented for every i = 1,2, ..., n, then L is also e-supplemented. If L is e-supplemented, then 1/a is also e-supplemented for every a is an element of L.