Weak c-ideals of a Lie algebra
TURKISH JOURNAL OF MATHEMATICS, cilt.45, ss.1940-1948, 2021 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 45
- Basım Tarihi: 2021
- Doi Numarası: 10.3906/mat-2006-55
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.1940-1948
- Anahtar Kelimeler: Weak c-ideal, Frattini ideal, Lie algebras, nilpotent, solvable, supersolvable, NORMAL SUBGROUPS, FINITE-GROUPS
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
A subalgebra B of a Lie algebra L is called a weak c-ideal of L if there is a subideal C of L such that L = B+C and B boolean AND C <= B-L where B-L is the largest ideal of L contained in B. This is analogous to the concept of weakly c-normal subgroups, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals.