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Weak c-ideals of a Lie algebra

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Weak c-ideals of a Lie algebra. / Towers, David; Ciloglu, Zekiye.
In: Turkish Journal of Mathematics, Vol. 45, No. 5, 16.09.2021, p. 1940-1948.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Towers, D & Ciloglu, Z 2021, 'Weak c-ideals of a Lie algebra', Turkish Journal of Mathematics, vol. 45, no. 5, pp. 1940-1948. https://doi.org/10.3906/mat-2006-55

APA

Towers, D., & Ciloglu, Z. (2021). Weak c-ideals of a Lie algebra. Turkish Journal of Mathematics, 45(5), 1940-1948. https://doi.org/10.3906/mat-2006-55

Vancouver

Towers D, Ciloglu Z. Weak c-ideals of a Lie algebra. Turkish Journal of Mathematics. 2021 Sept 16;45(5):1940-1948. doi: 10.3906/mat-2006-55

Author

Towers, David ; Ciloglu, Zekiye. / Weak c-ideals of a Lie algebra. In: Turkish Journal of Mathematics. 2021 ; Vol. 45, No. 5. pp. 1940-1948.

Bibtex

@article{a871643cc8ee4c37ab284b884343300b,
title = "Weak c-ideals of a Lie algebra",
abstract = "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∩C ≤ BL where BL 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.",
keywords = "Weak c-ideal, Frattini ideal, Lie algebras, nilpotent, solvable, supersolvable",
author = "David Towers and Zekiye Ciloglu",
year = "2021",
month = sep,
day = "16",
doi = "10.3906/mat-2006-55",
language = "English",
volume = "45",
pages = "1940--1948",
journal = "Turkish Journal of Mathematics",
issn = "1300-0098",
publisher = "TUBITAK",
number = "5",

}

RIS

TY - JOUR

T1 - Weak c-ideals of a Lie algebra

AU - Towers, David

AU - Ciloglu, Zekiye

PY - 2021/9/16

Y1 - 2021/9/16

N2 - 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∩C ≤ BL where BL 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.

AB - 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∩C ≤ BL where BL 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.

KW - Weak c-ideal

KW - Frattini ideal

KW - Lie algebras

KW - nilpotent

KW - solvable

KW - supersolvable

U2 - 10.3906/mat-2006-55

DO - 10.3906/mat-2006-55

M3 - Journal article

VL - 45

SP - 1940

EP - 1948

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

SN - 1300-0098

IS - 5

ER -