2022/08/06 by Marco Castelli, Castelli, Marco · 1 citation
Mathematics · #16T25 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2208.03490
openalex publication_date 2022/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study some relations between left cancellative left semi-braces and other existing algebraic structures. In particular, we show that every left semi-brace arises from a left seminear-ring, extending the correspondence given by Rump between skew left braces and left near-rings in \citerump2019set. Moreover, we show a correspondence between certain groups semidirect products and left cancellative left semi-braces satisfying an additional hypothesis on the set of idempotents. As an application, we classify left cancellative left semi-braces of size pq and 2p2 such that the set of idempotents E is a Sylow subgroup of the multiplicative group. Finally, we study various type of nilpotency, recently introduced in \citecatino2022nilpotency, of these left semi-braces.