On the passage from finite braces to pre-Lie rings

Autor: Agata Smoktunowicz

Let p be a prime number. We show that there is a one-to-one correspondence between the set of strongly nilpotent braces and the set of nilpotent pre-Lie rings of cardinality $p^{n}$, for sufficiently large p. Moreover, there is an injective mapping f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::19e47d90f4fd2120623f17b08b89d403
http://arxiv.org/abs/2202.00085

Five solved problems on radicals of Ore extensions

Autor: Michał Ziembowski, Be'eri Greenfeld, Agata Smoktunowicz

Publikováno v: Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Publ. Mat. 63, no. 2 (2019), 423-444
Greenfeld, B, Smoktunowicz, A & Ziembowski, M 2019, ' Five solved problems on radicals of Ore extensions ', Publicacions Matemàtiques, vol. 63, no. 2, pp. 423-444 . https://doi.org/10.5565/PUBLMAT6321902
Publicacions Matemàtiques; Vol. 63, Núm. 2 (2019); p. 423-444

The first named author was partially supported by an ISF grant #1623/16. The second named author was supported by ERC Advanced grant Coimbra 320974. The third named author was supported by the Polish National Science Centre grant UMO2017/25/B/ST1/003

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::279696dfb7e5cc21f632fa72c3d88c4c
https://doi.org/10.5565/publmat6321902

Algebraic approach to Rump’s results on relations between braces and pre-Lie algebras

Autor: Agata Smoktunowicz

Publikováno v: Smoktunowicz, A 2020, ' Algebraic approach to Rump’s results on relations between braces and pre-Lie algebras ', Journal of algebra and its applications, vol. 21, no. 3, 2250054 . https://doi.org/10.1142/S0219498822500542

In 2014, Wolfgang Rump showed that there exists a correspondence between left nilpotent right [Formula: see text]-braces and pre-Lie algebras. This correspondence, established using a geometric approach related to flat affine manifolds and affine tor

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d0b6a07b26579ad0bd8e42c30f38ac5
https://www.pure.ed.ac.uk/ws/files/180314305/NewAgata.pdf

Set-theoretic solutions of the Yang–Baxter equation and new classes of R-matrices

Autor: Alicja Smoktunowicz, Agata Smoktunowicz

Publikováno v: Linear Algebra and its Applications. 546:86-114

We describe several methods of constructing R-matrices that are dependent upon many parameters, for example unitary R-matrices and R-matrices whose entries are functions. As an application, we construct examples of R-matrices with prescribed singular

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::4d6fc43d2be01b8deb2d2a6c4d776f3a
https://doi.org/10.1016/j.laa.2018.02.001

How far can we go with Amitsur’s theorem in differential polynomial rings?

Autor: Agata Smoktunowicz

Publikováno v: Israel Journal of Mathematics. 219:555-608

A well-known theorem by S. A. Amitsur shows that the Jacobson radical of the polynomial ring R[x] equals I[x] for some nil ideal I of R. In this paper, however, we show that this is not the case for differential polynomial rings, by proving that ther

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d28e182acd2096a177a44954a2ee826d
https://doi.org/10.1007/s11856-017-1491-1