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Weak c-ideals of Leibniz algebras

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Weak c-ideals of Leibniz algebras. / Towers, David; ÇİLOĞLU ŞAHİN, Zekiye.
In: Communications in Algebra, Vol. 51, No. 11, 30.11.2023, p. 4676-4685.

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

Harvard

Towers, D & ÇİLOĞLU ŞAHİN, Z 2023, 'Weak c-ideals of Leibniz algebras', Communications in Algebra, vol. 51, no. 11, pp. 4676-4685. https://doi.org/10.1080/00927872.2023.2215340

APA

Towers, D., & ÇİLOĞLU ŞAHİN, Z. (2023). Weak c-ideals of Leibniz algebras. Communications in Algebra, 51(11), 4676-4685. https://doi.org/10.1080/00927872.2023.2215340

Vancouver

Towers D, ÇİLOĞLU ŞAHİN Z. Weak c-ideals of Leibniz algebras. Communications in Algebra. 2023 Nov 30;51(11):4676-4685. Epub 2023 May 25. doi: 10.1080/00927872.2023.2215340

Author

Towers, David ; ÇİLOĞLU ŞAHİN, Zekiye. / Weak c-ideals of Leibniz algebras. In: Communications in Algebra. 2023 ; Vol. 51, No. 11. pp. 4676-4685.

Bibtex

@article{9611928b735441a7825c4d99277af915,
title = "Weak c-ideals of Leibniz algebras",
abstract = "A subalgebra B of a Leibniz algebra L is called a weak c-ideal ofL if there is a subideal C of L such that L = B + C and B ∩ C ⊆ BLwhere BL is the largest ideal of L contained in B. This is analogousto the concept of a weakly c-normal subgroup, which has been studiedby a number of authors. We obtain some properties of weak c-idealsand use them to give some characterisations of solvable and supersolvable Leibniz algebras generalising previous results for Lie algebras. Wenote that one-dimensional weak c-ideals are c-ideals, and show that aresult of Turner classifying Leibniz algebras inwhich every one-dimensional subalgebra is a c-ideal is false for generalLeibniz algebras, but holds for symmetric ones.",
author = "David Towers and {{\c C}İLOĞLU {\c S}AHİN}, Zekiye",
year = "2023",
month = nov,
day = "30",
doi = "10.1080/00927872.2023.2215340",
language = "English",
volume = "51",
pages = "4676--4685",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "11",

}

RIS

TY - JOUR

T1 - Weak c-ideals of Leibniz algebras

AU - Towers, David

AU - ÇİLOĞLU ŞAHİN, Zekiye

PY - 2023/11/30

Y1 - 2023/11/30

N2 - A subalgebra B of a Leibniz algebra L is called a weak c-ideal ofL if there is a subideal C of L such that L = B + C and B ∩ C ⊆ BLwhere BL is the largest ideal of L contained in B. This is analogousto the concept of a weakly c-normal subgroup, which has been studiedby a number of authors. We obtain some properties of weak c-idealsand use them to give some characterisations of solvable and supersolvable Leibniz algebras generalising previous results for Lie algebras. Wenote that one-dimensional weak c-ideals are c-ideals, and show that aresult of Turner classifying Leibniz algebras inwhich every one-dimensional subalgebra is a c-ideal is false for generalLeibniz algebras, but holds for symmetric ones.

AB - A subalgebra B of a Leibniz algebra L is called a weak c-ideal ofL if there is a subideal C of L such that L = B + C and B ∩ C ⊆ BLwhere BL is the largest ideal of L contained in B. This is analogousto the concept of a weakly c-normal subgroup, which has been studiedby a number of authors. We obtain some properties of weak c-idealsand use them to give some characterisations of solvable and supersolvable Leibniz algebras generalising previous results for Lie algebras. Wenote that one-dimensional weak c-ideals are c-ideals, and show that aresult of Turner classifying Leibniz algebras inwhich every one-dimensional subalgebra is a c-ideal is false for generalLeibniz algebras, but holds for symmetric ones.

U2 - 10.1080/00927872.2023.2215340

DO - 10.1080/00927872.2023.2215340

M3 - Journal article

VL - 51

SP - 4676

EP - 4685

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 11

ER -