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On fraction-dense algebraic frames

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Abstract

We abstract the notion of fraction-density of f-rings (introduced by Anthony Hager and Jorge Martínez) to algebraic frames. We say an algebraic frame with the finite intersection property on compact elements is fraction-dense if each of its polars is a polar of a compact element. This turns out to be a “conservative” extension of the fraction-density property in the sense that a reduced f-ring is fraction-dense precisely when its frame of radical ideals is fraction-dense. We characterize these frames and study properties of some other types of algebraic frames that arise naturally in the characterizations of the fraction-dense ones.

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Authors and Affiliations

  1. Department of Mathematical Sciences Charles E. Schmidt College of Science, Florida Atlantic University, Boca Raton, FL, 33431, USA

    Papiya Bhattacharjee

  2. Department of Mathematical Sciences, University of South Africa, P.O. Box 392 , Pretoria, 0003, South Africa

    Themba Dube

Authors
  1. Papiya Bhattacharjee
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  2. Themba Dube
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Correspondence to Papiya Bhattacharjee.

Additional information

Presented by V. Marra

In memory of Professor Jorge Martínez.

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Dube acknowledges funding from the National Research Foundation of South Africa under Grant Number 113829.

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Bhattacharjee, P., Dube, T. On fraction-dense algebraic frames. Algebra Univers. 83, 6 (2022). https://doi.org/10.1007/s00012-021-00763-0

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  • DOI: https://doi.org/10.1007/s00012-021-00763-0

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