STRONGLY FULLY INVARIANT-EXTENDING MODULAR LATTICES

Albu T., KARA ŞEN Y., TERCAN A.

QUAESTIONES MATHEMATICAE, cilt.45, sa.3, ss.357-367, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 3
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2989/16073606.2020.1861488
  • Dergi Adı: QUAESTIONES MATHEMATICAE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.357-367
  • Anahtar Kelimeler: Modular lattice, upper continuous lattice, linear morphism of lattices, fully invariant element, fully invariant-extending lattice, strongly fully invariant-extending lattice
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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).