Let $(R,\mathfrak{m})$ be a Noetherian local domain, let $K(R)$ be the total fraction field of $R$ and let $R^{+}$ the absolute integral closure of $R$. Consider the $R$-module $K(R)\otimes_{R} R^{+}$ via extension of scalars. Let $J$ be the ideal $\mathfrak{m}R^{+}$ of $R^{+}$. I don't know if $J(K(R)\otimes_{R} R^{+})=K(R)\otimes_{R} R^{+}$.