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Let $R$ be a lattice ordered ring along with a truncation in the sense ofBall. We give a necessary and sufficient condition on $R$ for its unitization$R\oplus\mathbb{Q}$ to be again a lattice ordered ring. Also, we shall see that$R\oplus\mathbb{Q}$ is a lattice ordered ring for at most one truncation.Particular attention will be paid to the Archimedean case. More precisely, weshall identify the unique truncation on an Archimedean $\ell$-ring $R$ whichmakes $R\oplus\mathbb{Q}$ into a lattice ordered ring.

Unitization of a lattice ordered ring with a truncation