Maximal d-Elements of an Algebraic Frame

Papiya Bhattacharjee

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)377-390
Number of pages14
JournalOrder
Volume36
Issue number2
DOIs
StatePublished - Jul 15 2019

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics

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