Rota–Baxter operators on Clifford semigroups and the Yang–Baxter equation

In this paper, we introduce the theory of Rota-Baxter operators on Clifford semigroups, useful tools for obtaining dual weak braces, i.e., triples $\left(S,+,\circ\right)$ where $\left(S,+\right)$ and $\left(S,\circ\right)$ are semigroups such that $a\circ\left(b+c\right) = a\circ b - a +a\circ c$ $a\circ a^- -a+a$, all $a,b,c\in S$. To each algebraic structure is associated set-theoretic solution Yang-Baxter equation has behaviour near to bijectivity non-degeneracy. Drawing from provide methods constructing braces deepen some structural aspects, including notion ideal.