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On the sobriety of the inverse topology

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Abstract

An algebraic frame L with the finite intersection property (FIP) on compact elements is said to be polarised if every minimal prime element in it is complemented. In this note, we give a necessary and sufficient condition for the inverse topology on the set of minimal prime elements of such a frame to be sober. We also establish some sufficient conditions for sobriety when the polarisation condition is relaxed.

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Authors and Affiliations

  1. School of Science, Penn State Erie - The Behrend College, Erie, PA, 16563, USA

    Papiya Bhattacharjee

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

    Themba Dube

Authors
  1. Papiya Bhattacharjee
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  2. Themba Dube
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Corresponding author

Correspondence to Papiya Bhattacharjee.

Additional information

Presented by C. Tsinakis.

The research of T.D. was supported by the National Research Foundation of South Africa under grant no. 93514.

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Bhattacharjee, P., Dube, T. On the sobriety of the inverse topology. Algebra Univers. 76, 445–454 (2016). https://doi.org/10.1007/s00012-016-0414-z

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  • DOI: https://doi.org/10.1007/s00012-016-0414-z

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