Oghenetega Ighedo

COMMENTS REGARDING d-IDEALS OF CERTAIN f-RINGS

Let A be a reduced commutative f-ring with identity and bounded inversion, and let A* be its subring of bounded elements. By first observing that A is the ring of fractions of A* relative to the subset of A* consisting of elements which are units in the bigger ring, we show that the frames Did(A) and Did(A*) of d-ideals of A and A*, respectively, are isomorphic, and that the isomorphism witnessing this is precisely the restriction of the extension map I ↦ Ie which takes a radical ideal of A* to the ideal it generates in A. Specializing to the ring

Two Functors Induced by Certain Ideals of Function Rings

\mathcal{R}L

On lattices of z-ideals of function rings

, we show that if L is an F-frame, then the saturation quotient of

More ring-theoretic characterizations of P-frames

{\rm Did}(\mathcal{R}L)

On some parallelism between complete regularity and zero-dimensionality

is isomorphic to βL. We also investigate projectability properties of

On

{\rm Did}(\mathcal{R}L)

z

and

-ideals of pointfree function rings

{\rm Zid}(\mathcal{R}L)

More on locales in which every open sublocale is z-embedded

, where the latter denotes the frame of z-ideals of

Higher order z-ideals in commutative rings

\mathcal{R}L