Rota–Baxter Operators on Skew Braces

Author:

Wang Ximu1,Zhang Chongxia1,Zhang Liangyun1

Affiliation:

1. Department of Mathematics, Nanjing Agricultural University, Nanjing 210095, China

Abstract

In this paper, we introduce the concept of Rota–Baxter skew braces, and provide classifications of Rota–Baxter operators on various skew braces, such as (Z,+,∘) and (Z/(4),+,∘). We also present a necessary and sufficient condition for a skew brace to be a co-inverse skew brace. Additionally, we describe some constructions of Rota–Baxter quasiskew braces, and demonstrate that every Rota–Baxter skew brace can induce a quasigroup and a Rota–Baxter quasiskew brace.

Publisher

MDPI AG

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