The nil radicals in several classes of lattice-ordered rings (Q5932692)

The author is interested in the nil radicals in a lattice-ordered ring. There are several \(l\)-radicals defined on lattice-ordered rings. Several conditions (for example, minimum or maximum condition on nil \(l\)-ideals, or positivity of the square of each element) are given to ensure that these radicals coincide with each other. The author also considers the Köthe problem for lattice-ordered rings, in particular, it is shown that the ideal generated by a nil one-sided ideal contained in a nil one-sided \(l\)-ideal is again nil.