Representations of algebras by continuous sections
@article{Hofmann1972RepresentationsOA, title={Representations of algebras by continuous sections}, author={Karl Heinrich Hofmann}, journal={Bulletin of the American Mathematical Society}, year={1972}, volume={78}, pages={291-373} }
This survey is concerned with the representation of discrete rings and topological algebras (such as C*-algebras) by rings of continuous sections in sheaves of rings or fields of topological algebras.
91 Citations
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The spectral radius of an element of aC0(X)-Banach algebra can be calculated as the supremum of the spectral radii in the fibres. As a consequence, calculations in K-theory for such algebras can…
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References
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- 1971
Throughout this paper we consider associative rings with unity elements. In §1 various results on the representation of rings by rings of sections of special rings are compared. In particular, it is…
On Functional Representations of a Ring without Nilpotent Elements
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- 1971
In [3, p. 149], J. Lambek gives a proof of a theorem, essentially due to Grothendieck and Dieudonne, that if R is a commutative ring with 1 then R is isomorphic to the ring of global sections of a…
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- 1971
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Stone's duality between Boolean algebras and Boolean spaces is extended to a dual equivalence between the category of all ^dimensional cylindric algebras and a certain category of sheaves of such…
Prime ideal structure in commutative rings
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0. Introduction. Let ' be the category of commutative rings with unit, and regard Spec (as in [1]) as a contravariant functor from ' to g$7 the category of topological spaces and continuous maps. The…
The Minimal Prime Spectrum of a Commutative Ring
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- 1971
We call a topological space X minspectral if it is homeomorphic to the space of minimal prime ideals of a commutative ring A in the usual (hull-kernel or Zariski) topology (see [2, p. 111]). Note…