GENERALIZATIONS OF COMPLEMENTED RINGS WITH APPLICATIONS TO RINGS OF FUNCTIONS

DOI10.1142/S0219498809003138zbMath1173.13002OpenAlexW1982475342MaRDI QIDQ3622759

Jay Shapiro, Warren Wm. McGovern, Ronnie Levy, Michelle L. Knox

Publication date: 28 April 2009

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498809003138

zbMATH Keywords

clean ringring of continuous real valued functions(weakly, quasi-)complemented ring

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Real-valued functions in general topology (54C30) Extremally disconnected spaces, (F)-spaces, etc. (54G05) Rings of fractions and localization for commutative rings (13B30)

Related Items (20)

A closer look at primal and pseudo-irreducible ideals with applications to rings of functions ⋮ Quasicomplemented residuated lattices ⋮ \(p\)-embeddings ⋮ On EM-spaces ⋮ On a theorem of Anderson and Chun ⋮ Commutative group rings with von Neumann regular total rings of quotients. ⋮ Fusible rings ⋮ The flat topology on the minimal and maximal prime spectrum of a commutative ring ⋮ TWO SPACES OF MINIMAL PRIMES ⋮ Concerning maximal \(\ell\)-ideals of rings of continuous integer-valued functions. ⋮ Structure theory of p.p. rings and their generalizations ⋮ Clean unital ℓ-groups ⋮ A characterization of von Neumann regular rings and applications. ⋮ C(X): Something old and something new ⋮ Locales whose coz-complemented cozero sublocales have open closures ⋮ On the lattice of \(z\)-ideals of a commutative ring ⋮ Zariski compactness of minimal spectrum and flat compactness of maximal spectrum ⋮ Lamron ℓ-groups ⋮ The Semilattice of Annihilator Classes in a Reduced Commutative Ring ⋮ Feebly Baer Rings and Modules

Cites Work

• Exchange PF-rings and almost PP-rings
• When is \(C(X)\) a clean ring?
• Neat rings
• Commutative coherent rings
• Rings of quotients of rings of functions
• Cozero complemented spaces; when the space of minimal prime ideals of a \(C(X)\) is compact
• Almost-P-Spaces
• Clean Semiprimef-Rings with Bounded Inversion

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