Ideal Connes-amenability of Lau product of Banach algebras

Let $\mathcal{A}$ and $\mathcal{B}$ be Banach algebras and $\theta$ be a non-zero character on $\mathcal{B}$. In the current paper, we study the ideal Connes-amenability of the algebra $\mathcal{A}\times_\theta\mathcal{B}$ so-called the $\tau$-Lau product algebra. We also prove that if $\mathcal{A}\times_\theta\mathcal{B}$ is ideally Connes-amenable, then both $\mathcal{A}$ and $\mathcal{B}$ are ideally Connes-amenable. As a result, we show that $l^1(S)\times_\theta l^1(S)$ is ideally Connes-amenable, where $S$ is a Rees matrix semigroup.