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Contribución al estudio de los anillos reticulados y f-anillos.

Joan Trías Pairó (1979)

Stochastica

This paper deals with ordered rings and f-rings. Some relations between classes of ideals are obtained. The idea of subunity allows us to study the possibility of embedding the ring in a unitary f-ring. The Boolean algebras of idempotents and lattice-isometries in an f-ring are studied. We give geometric characterizations of the l-isometries and obtain, in the projectable case, that the Stone space of the Boolean algebra of l-isometries is homeomorphic to the space of minimal prime ideals with the...

Dimension in algebraic frames

Jorge Martinez (2006)

Czechoslovak Mathematical Journal

In an algebraic frame L the dimension, dim ( L ) , is defined, as in classical ideal theory, to be the maximum of the lengths n of chains of primes p 0 < p 1 < ⋯ < p n , if such a maximum exists, and ∞ otherwise. A notion of “dominance” is then defined among the compact elements of L , which affords one a primefree way to compute dimension. Various subordinate dimensions are considered on a number of frame quotients of L , including the frames d L and z L of d -elements and z -elements, respectively. The more concrete illustrations...

Domination properties in ordered Banach algebras

H. du T. Mouton, S. Mouton (2002)

Studia Mathematica

We recall from [9] the definition and properties of an algebra cone C of a real or complex Banach algebra A. It can be shown that C induces on A an ordering which is compatible with the algebraic structure of A. The Banach algebra A is then called an ordered Banach algebra. An important property that the algebra cone C may have is that of normality. If C is normal, then the order structure and the topology of A are reconciled in a certain way. Ordered Banach algebras have interesting spectral properties....

Faithfully quadratic rings - a summary of results

M. Dickmann, F. Miraglia (2016)

Banach Center Publications

This is a summary of some of the main results in the monograph Faithfully Ordered Rings (Mem. Amer. Math. Soc. 2015), presented by the first author at the ALANT conference, Będlewo, Poland, June 8-13, 2014. The notions involved and the results are stated in detail, the techniques employed briefly outlined, but proofs are omitted. We focus on those aspects of the cited monograph concerning (diagonal) quadratic forms over preordered rings.

Finitely valued f -modules, an addendum

Stuart A. Steinberg (2001)

Czechoslovak Mathematical Journal

In an ℓ -group M with an appropriate operator set Ω it is shown that the Ω -value set Γ Ω ( M ) can be embedded in the value set Γ ( M ) . This embedding is an isomorphism if and only if each convex ℓ -subgroup is an Ω -subgroup. If Γ ( M ) has a.c.c. and M is either representable or finitely valued, then the two value sets are identical. More generally, these results hold for two related operator sets Ω 1 and Ω 2 and the corresponding Ω -value sets Γ Ω 1 ( M ) and Γ Ω 2 ( M ) . If R is a unital ℓ -ring, then each unital ℓ -module over R is an f -module...

Currently displaying 21 – 40 of 151