Some algebraic characterizations of \(F\)-frames

DOI10.1007/s00012-010-0054-7zbMath1225.06007OpenAlexW2056704974MaRDI QIDQ987185

Themba Dube

Publication date: 13 August 2010

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00012-010-0054-7

zbMATH Keywords

Bézout ringcompletely regular frame\(F\)-framealmost weak Baer ringrings of continuous functions on a framestrongly zero-dimensional frame

Mathematics Subject Classification ID

Frames, locales (06D22) Extremally disconnected spaces, (F)-spaces, etc. (54G05)

Related Items

Quasi SV-frames and their properties, A lattice-theoretic view of some special ideals of subrings of commutative rings, Unnamed Item, zc-ideals and prime ideals in the ring RcL, Unnamed Item, Unnamed Item, On ideals of rings of continuous functions associated with sublocales, Finite frames, \(P\)-frames and basically disconnected frames, Concerning real-closed ideals in \(\mathcal{R} L\) and SV-frames, Characterizing realcompact locales via remainders, On quasi-normality of function rings, Some new characterizations of finite frames and \(F\)-frames, Coherence classes of ideals of normal lattices with applications to C(X), \(z\)-ideals in the real continuous function ring \(\mathcal{R}(L_{\tau}) \), Covering maximal ideals with minimal primes, On the maximal regular ideal of pointfree function rings, and more, More ring-theoretic characterizations of P-frames, Notes Concerning Characterizations of Quasi-FFrames, Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame, Concerning \(P\)-frames, essential \(P\)-frames, and strongly zero-dimensional frames, Some notes on \(z\)-ideal and \(d\)-ideal in \(\mathcal{R}L\), Ideals of functions with compact support in the integer-valued case, ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS, A note on spaces that are finitely an \(F\)-space.

Cites Work

• Unnamed Item
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• On the function ring functor in pointfree topology
• Some notes on \(C\)- and \(C^*\)-quotients of frames
• Concerning \(P\)-frames, essential \(P\)-frames, and strongly zero-dimensional frames
• Some ring-theoretic properties of almost \(P\)-frames
• Sheaves of integral domains on Stone spaces
• A uniform view of localic realcompactness
• Notes on pointfree disconnectivity with a ring-theoretic slant
• F'-spaces and z-embedded subspaces
• On two sum theorems for ideals of \(C(X)\)
• Coz-onto frame maps and some applications
• Rings of Continuous Functions in Which Every Finitely Generated Ideal is Principal
• Samuel compactification and completion of uniform frames
• Lindelöf locales and realcompactness
• Bezout and prufer f-rings
• C- and C^*-quotients in pointfree topology