Unitization of a lattice ordered ring with a truncation
Abstract
Let R be a lattice ordered ring along with a truncation in the sense of Ball. We give a necessary and sufficient condition on R for its unitization R to be again a lattice ordered ring. Also, we shall see that R is a lattice ordered ring for at most one truncation. Particular attention will be paid to the Archimedean case. More precisely, we shall identify the unique truncation on an Archimedean -ring R which makes R into a lattice ordered ring.
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