## 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 language | English (US) |
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Pages (from-to) | 377-390 |

Number of pages | 14 |

Journal | Order |

Volume | 36 |

Issue number | 2 |

DOIs | |

State | Published - Jul 15 2019 |

## All Science Journal Classification (ASJC) codes

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