Some notes on \(z\)-ideal and \(d\)-ideal in \(\mathcal{R}L\)

DOI10.1007/s41980-019-00278-4zbMath1437.06012OpenAlexW2969575379MaRDI QIDQ779707

Mostafa Abedi

Publication date: 14 July 2020

Published in: Bulletin of the Iranian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41980-019-00278-4

zbMATH Keywords

frame\(z\)-idealextremally disconnected frame\(P\)-framebasically disconnected frame\(d\)-idealalmost \(P\)-framequasi \(F\)-frame

Mathematics Subject Classification ID

Frames, locales (06D22) Ideals and multiplicative ideal theory in commutative rings (13A15) Extremally disconnected spaces, (F)-spaces, etc. (54G05) (P)-spaces (54G10)

Related Items (3)

Unnamed Item ⋮ Unnamed Item ⋮ Concerning \(P\)-frames and the Artin-Rees property

Cites Work

• On \(z\)-ideals of pointfree function rings
• When certain prime ideals in rings of continuous functions are minimal or maximal.
• Some algebraic characterizations of \(F\)-frames
• Concerning \(P\)-frames, essential \(P\)-frames, and strongly zero-dimensional frames
• Some ring-theoretic properties of almost \(P\)-frames
• On injectivity of the ring of real-valued continuous functions on a frame
• Notes on pointfree disconnectivity with a ring-theoretic slant
• A new aspect of the cozero lattice in pointfree topology
• Zero sets in pointfree topology and strongly \(z\)-ideals
• z-ideals and prime ideals
• \(\sqrt z\)-ideals and \(\sqrt {z^{^\circ}}\)-ideals in \(C(X)\)
• Frames and Locales
• Notes Concerning Characterizations of Quasi-FFrames
• Prime z-Ideals of C(X) and Related Rings
• On lattices of z-ideals of function rings
• A note on weakly Lindelöf frames
• C- and C^*-quotients in pointfree topology
• On ideals consisting entirely of zero divisors
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