STRONGLY FULLY INVARIANT-EXTENDING MODULAR LATTICES


Albu T., KARA ŞEN Y., TERCAN A.

QUAESTIONES MATHEMATICAE, vol.45, no.3, pp.357-367, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.2989/16073606.2020.1861488
  • Journal Name: QUAESTIONES MATHEMATICAE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.357-367
  • Keywords: Modular lattice, upper continuous lattice, linear morphism of lattices, fully invariant element, fully invariant-extending lattice, strongly fully invariant-extending lattice
  • Hacettepe University Affiliated: Yes

Abstract

This paper is a natural continuation of our previous joint paper [Albu, Kara, Tercan, Fully invariant-extending modular lattices, and applications (I), J. Algebra 517 (2019), 207-222], where we introduced and investigated the notion of a fully invariant-extending lattice, the latticial counterpart of a fully invariant-extending module. In this paper we introduce and investigate the latticial counter-part of the concept of a strongly FI-extending module defined by Birkenmeier, Park, Rizvi (2002) as a module M having the property that every fully invariant submodule of M is essential in a fully invariant direct summand of M. Our main tool in doing so, is again the very useful concept of a linear morphism of lattices introduced in the literature by Albu and Iosif (2013).