8 papers
Analogues of Grün's lemma and Baer's theorem for skew left braces
A. Ballester-Bolinches, R. Esteban-Romero, L. A. Kurdachenko +1
We prove in this paper some analogues of the well-known group-theoretical Grün's lemma, stating that in a perfect group the first and the second centre coincide, and Baer's theore…
On left braces in which every subbrace is an ideal II
A. Ballester-Bolinches, R. Esteban-Romero, L. A. Kurdachenko +1
The aim of this paper is to take the study of Dedekind braces, that is, left braces for which every subbrace is an ideal, started in a previous paper, further. Dedekind braces …
Leibniz rings: some basic and structural results
L. A. Kurdachenko, O. O. Pypka, M. M. Semko
In this paper, we study the fundamental properties of Leibniz rings. Special attention is given to the structure of Leibniz rings whose additive group is "small". The results obtai…
On the structure of braces whose subideals are ideals
Martyn R. Dixon, Leonid A. Kurdachenko, Igor Ya. Subbotin
This article begins the study of T-braces, those skew left braces of abelian type in which the relation of being an ideal is a transitive relation.
On finitely generated left nilpotent braces
H. Meng, A. Ballester-Bolinches, L. A. Kurdachenko +1
A description of finitely generated left nilpotent braces of class at most two is presented in this paper. The description heavily depends on the fact that if is left nilpotent…
On left nilpotent skew braces of class 2
A. Ballester-Bolinches, L. A. Kurdachenko, V. Pérez-Calabuig
The main objective of this article is to initiate a detailed structure theory of left nilpotent skew braces of class , i.e. skew braces with . We prove that if …