Copies of $\ell_{\infty}$ in quotients of locally solid Riesz spaces

Abstract.

Let $E = (E, \tau)$ be a locally solid Riesz space containing a lattice copy of $\ell_{\infty}$, and let M be a $\tau$-closed and Dedekind $\sigma$-complete ideal of E. Then E/M or M contains a lattice copy of $\ell_{\infty}$ (Theorem 1). If E is Dedekind $\sigma$-complete and E _a denotes the Lebesgue ideal of E, then the quotient Riesz space E/E _a contains a lattice copy of $\ell_{\infty}$ whenever $\tau$ is not pre-Lebesgue (Corollary 1).