The f-radical of a lattice-ordered ring R is the l-ring analogue of the Jacobson radical of a ring. It is shown that if the matrix ring R-n has the usual lattice order, then f (R-n) = f (R)(n). The connection between an element a being right e-quasi-regular and the inequality a 0 x less than or equal to 0 is also investigated. For squares in an f-ring the connection is an equivalence. In general it is still an equivalence provided x is the sum of elements from a larger f-ring whose absolute values lie in R. It is also shown that the vanishing of annihilators in an f-ring is inherited by enough totally ordered homomorphic images to give a subdirect product decomposition. [References: 13]
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