The Nil Radicals in Several Classes of Lattice-Ordered Rings

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Abstract

We characterize the nil radicals in some l-rings. Several sufficient conditions for the nil radicals of l-rings to be equal and nilpotent are given. The results improve corresponding ones of Birkhoff and Pierce. We also show that the ideal generated by a nil one-sided ideal which is contained in a nil one-sided l-ideal is nil.

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