Browsing by Author "Albu, Toma"
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Publication Fully invariant-extending modular lattices, and applications (I)(Elsevier, 2019-01-01) Albu, Toma; Kara, Yeliz; Tercan, Adnan; KARA ŞEN, YELİZ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-8001-6082; AAG-8304-2021Based on the concept of a linear morphism of lattices, recently introduced in the literature, we introduce and investigate in this paper the latticial counterpart of the notion of a fully invariant-extending module. (C) 2018 Elsevier Inc. All rights reserved.Publication Strongly fully invariant-extending modular lattices(Taylor, 2021-01-20) Albu, Toma; Kara, Yeliz; Tercan, Adnan; KARA ŞEN, YELİZ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-8001-6082; AAG-8304-2021This 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).