Regular division closed lattice-ordered rings

Abstract

We provide an example of a regular division closed commutative lattice ordered ring with identity element that is not an almost f-ring. It is also pointed out that regular division closed commutative lattice-ordered rings with the identity element are f-rings provided they contain only a finite number of maximal ideals.

Key words: Almost f-ring, commutative ℓ-ring, lattice order, regular division closed.