| dc.creator |
Ismailov, N. A. |
|
| dc.creator |
Sartayev, B. K. |
|
| dc.creator |
Dzhumadil'daev, A. S. |
|
| dc.date |
2022-06-01T00:00:00Z |
|
| dc.date.accessioned |
2023-01-09T12:05:43Z |
|
| dc.date.available |
2023-01-09T12:05:43Z |
|
| dc.identifier |
98e22027-c773-4ea9-b310-7a3cfb7f3960 |
|
| dc.identifier |
10.1142/s0218196722500333 |
|
| dc.identifier |
https://avesis.sdu.edu.tr/publication/details/98e22027-c773-4ea9-b310-7a3cfb7f3960/oai |
|
| dc.identifier.uri |
http://acikerisim.sdu.edu.tr/xmlui/handle/123456789/98148 |
|
| dc.description |
We prove that the class of algebras embeddable into Leibniz algebras with respect to the commutator product is not a variety. It is shown that every commutative metabelain algebra is embeddable into Leibniz algebras with respect to the anti-commutator. Furthermore, we study polynomial identities satisfied by the commutator in every Leibniz algebra. We extend the result of Dzhumadil'daev in [A. S. Dzhumadil'daev, q-Leibniz algebras, Serdica Math. J. 34(2) (2008) 415-440]. to identities up to degree 7 and give a conjecture on identities of higher degrees. As a consequence, we obtain an example of a non-Spechtian variety of anticommutative algebras. |
|
| dc.language |
eng |
|
| dc.rights |
info:eu-repo/semantics/closedAccess |
|
| dc.title |
On the commutator in Leibniz algebras |
|
| dc.type |
info:eu-repo/semantics/article |
|