Algebras and spaces of dense constancies

Angelo Bella; Jorge Martinez; Scott D. Woodward

Displaying similar documents to “Algebras and spaces of dense constancies”

Real holomorphy rings and the complete real spectrum

D. Gondard, M. Marshall (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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The complete real spectrum of a commutative ring $A$ with $1$ is introduced. Points of the complete real spectrum ${Sper}^{c} A$ are triples $α = (𝔭, v, P)$ , where $𝔭$ is a real prime of $A$ , $v$ is a real valuation of the field $k (𝔭) : = qf (A / 𝔭)$ and $P$ is an ordering of the residue field of $v$ . ${Sper}^{c} A$ is shown to have the structure of a spectral space in the sense of Hochster []. The specialization relation on ${Sper}^{c} A$ is considered. Special attention is paid to the case where the ring $A$ in question is a real holomorphy ring.

Isomorphism with a C(Y) of the maximal ring of quotients of C(X)

Anthony Hager (1970)

Fundamenta Mathematicae

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When is every order ideal a ring ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith (1991)

Commentationes Mathematicae Universitatis Carolinae

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A lattice-ordered ring $ℝ$ is called an if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those $f$ -rings $ℝ$ such that $ℝ / 𝕀$ is contained in an $f$ -ring with an identity element that is a strong order unit for some nil $l$ -ideal $𝕀$ of $ℝ$ . In particular, if $P (ℝ)$ denotes the set of nilpotent elements of the $f$ -ring $ℝ$ , then $ℝ$ is an OIRI-ring if and only if $ℝ / P (ℝ)$ is contained in an $f$ -ring with an identity element that is a strong order unit. ...

Arens regularity of lattice-ordered rings

Karim Boulabiar, Jamel Jabeur (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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This work discusses the problem of Arens regularity of a lattice-ordered ring. In this prospect, a counterexample is furnished to show that without extra conditions, a lattice-ordered ring need not be Arens regular. However, as shown in this paper, it turns out that any $f$ -ring in the sense of Birkhoff and Pierce is Arens regular. This result is then used and extended to the more general setting of almost $f$ -rings introduced again by Birkhoff.