The space of maximal d-ideals of C(X) is well-known and is widely studied. It is known that the space of maximal d-ideals is homeomorphic to the Z♯(X)-ultrafilters, and this space is the minimal quasi F-cover of a compact Tychonoff space X. In the current article we generalize this concept for M-frames, algebraic frames with the finite intersection property. In particular, we explore various properties of the maximal d-elements of a frame L, and their relation with the ultrafilters of 픎L⊥, the polars of the compact elements of L. On a separate note, we revisit the Lemma on Ultrafilters and establish the correspondence between the minimal prime elements spaces of L with the spaces of ultrafilters of 픎L. Finally, we show that for complemented frames L, Min(L) = Max(dL), a result parallel to the one known for Riesz spaces, W-objects, and topological spaces.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology
- Computational Theory and Mathematics