| Title:
|
Existentially closed Leibniz algebras and an embedding theorem (English) |
| Author:
|
Zargeh, Chia |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
163-170 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem. (English) |
| Keyword:
|
Existentially closed |
| Keyword:
|
Leibniz algebras |
| Keyword:
|
HNN-extension |
| MSC:
|
16S15 |
| MSC:
|
17A32 |
| MSC:
|
17A36 |
| idZBL:
|
Zbl 07426415 |
| idMR:
|
MR4285748 |
| . |
| Date available:
|
2021-11-04T12:09:00Z |
| Last updated:
|
2021-12-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149185 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Higman, G., Neumann, B. H., Neumann, H.: Embedding theorems for groups.J. London. Math. Soc, 24, 1949, 247-254, 10.1112/jlms/s1-24.4.247 |
| Reference:
|
[4] Higman, G., Scotty, E. L.: Existentially closed groups.1988, Clarendon Press, |
| Reference:
|
[5] Kolesnikov, P. S., Makar-Limanov, L. G., Shestakov, I. P.: The Freiheitssatz for Generic Poisson Algebras.SIGMA, 10, 2014, 115-130, |
| Reference:
|
[6] Ladra, M., Páez-Guillán, P., Zargeh, C.: HNN-extension of Lie superalgebras.Bull. Malays. Math. Sci. Soc., 43, 2020, 1959-1970, 10.1007/s40840-019-00783-z |
| Reference:
|
[7] Ladra, M., Shahryari, M., Zargeh, C.: HNN-extensions of Leibniz algebras.Journal of Algebra, 532, 12, 2019, 183-200, 10.1016/j.jalgebra.2019.05.014 |
| Reference:
|
[8] J.,-L, Loday: Une Version non commutative des algebras de Lie: les algebras de Leibniz.Enseign. Math., 39, 1993, 269-293, |
| Reference:
|
[9] Lyndon, R. C., Schupp, P. E.: Combinatorial Group Theory.2001, Springer-Verlag, New York, Zbl 0997.20037 |
| Reference:
|
[10] Scott, W. R.: Algebraically closed groups.Proc. of AMS, 1, 2, 1951, 118-121, |
| Reference:
|
[11] Shahryari, M.: Existentially closed structures and some embedding theorems.Mathematical Notes, 101, 6, 2017, 1023-1032, 10.1134/S0001434617050297 |
| Reference:
|
[12] Silvestrov, S., Zargeh, C.: HNN-extension of involutive multiplicative Hom-Lie algebras.arXiv:2101.01319 [math.RA], 2021, preprint. |
| . |
