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Mathematics > Rings and Algebras

arXiv:2202.00085 (math)
[Submitted on 31 Jan 2022 (v1), last revised 28 Apr 2022 (this version, v3)]

Title:On the passage from finite braces to pre-Lie rings

Authors:Agata Smoktunowicz
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Abstract: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 from the set of left nilpotent pre-Lie rings into the set of left nilpotent braces of cardinality $p^{n}$ for n+1<p. For the passage from pre-Lie rings to braces we use exactly the same method as suggested in [41].
Comments: arXiv admin note: text overlap with arXiv:2011.07611 Some assumptions were removed from Lemma 15 answering Question 3, also Question 3 was removed.A gap in the proof of Theorem 2 was corrected
Subjects: Rings and Algebras (math.RA)
MSC classes: 17A65, 17D99, 20F18, 20F40
Cite as: arXiv:2202.00085 [math.RA]
  (or arXiv:2202.00085v3 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.2202.00085

Submission history

From: Agata Smoktunowicz [view email]
[v1] Mon, 31 Jan 2022 20:53:11 UTC (17 KB)
[v2] Wed, 23 Feb 2022 10:08:07 UTC (21 KB)
[v3] Thu, 28 Apr 2022 10:47:21 UTC (23 KB)
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