Weak c-ideals of Leibniz algebras
Communications in Algebra, cilt.51, sa.11, ss.4676-4685, 2023 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 51 Sayı: 11
- Basım Tarihi: 2023
- Doi Numarası: 10.1080/00927872.2023.2215340
- Dergi Adı: Communications in Algebra
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
- Sayfa Sayıları: ss.4676-4685
- Anahtar Kelimeler: Frattini ideal, Leibniz algebra, Solvable, Supersolvable, Symmetric Leibniz algebra, Weak c-ideal
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
A subalgebra B of a Leibniz algebra L is called a weak c-ideal of L if there is a subideal C of L such that (Formula presented.) and (Formula presented.) where (Formula presented.) is the largest ideal of L contained in B. This is analogous to the concept of a weakly c-normal subgroup, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterizations of solvable and supersolvable Leibniz algebras generalizing previous results for Lie algebras. We note that one-dimensional weak c-ideals are c-ideals, and show that a result of Turner classifying Leibniz algebras in which every one-dimensional subalgebra is a c-ideal is false for general Leibniz algebras, but holds for symmetric ones.