Rigid extensions of algebraic frames

Papiya Bhattacharjee

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

An extension G ≤ H of lattice-ordered groups is said to be a rigid extension if for each H ∈ H there exists a g ∈ G such that h⊥⊥ = g⊥⊥. In this paper, we will define rigid extensions and some other generalizations in the context of algebraic frames satisfying the FIP. One of the main results is a characterization of rigid extensions using d-elements of the frame. We also show that a rigid extension between two algebraic frames satisfying the FIP will induce a homeomorphism between their corresponding minimal prime spaces with respect to both the hull-kernel topology and the inverse topology. Moreover, basic open sets map to basic open sets.

Original languageEnglish (US)
Pages (from-to)133-149
Number of pages17
JournalAlgebra Universalis
Volume62
Issue number1
DOIs
StatePublished - Dec 2009

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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