Division closed lattice-ordered rings and commutative L*-rings

Abstract

The paper continues the study of division closed lattice-ordered rings and commutative L*-rings. More interesting properties of division closed lattice- ordered rings are presented and it is shown that under certain conditions such rings are f-rings. The main result on L*-rings is that for a commutative semilocal ring with the identity, it is L* if and only if it is O*.

Mathematics Subject Classification (2010): Primary 06F25.

Keywords: Lattice order, partial order, regular division closed, total order, F*-ring, L*-ring, O*-ring