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}
}
  • K. Hofmann
  • Published 1 May 1972
  • Mathematics
  • Bulletin of the American Mathematical Society
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. 

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References

SHOWING 1-10 OF 76 REFERENCES
On the Representation of Modules by Sheaves of Factor Modules
  • J. Lambek
  • Mathematics
    Canadian Mathematical Bulletin
  • 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
  • Kwangil Koh
  • Mathematics
    Canadian Mathematical Bulletin
  • 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
The Space of Minimal Prime Ideals of a Commutative Ring
Introduction. Of the various spaces of ideal of rings that have been studied (see [1 ], for example) we are focusing attention on the space of minimal prime ideals because of its special role in the
Rings with orthogonality relations
  • G. Davis
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 1971
The rings of this paper are assumed to have relations of orthogonality defined on them. Such relations are uniquely determined by complete boolean algebras of ideals. Using the Stone space of these
Vector bundles and projective modules
Serre [9, ?50] has shown that there is a one-to-one correspondence between algebraic vector bundles over an affine variety and finitely generated projective modules over its coordinate ring. For some
TOPOLOGICAL REPRESENTATION OF C*-ALGEBRAS
Let A be a C*-algebra, ίl the structure space of A, i.e. the space of all primitive ideals in A with hull-kernel topology. At every point P of ί l we associate a primitive C^-algebra A/P (which we
A sheaf-theoretic duality theory for cylindric algebras
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
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
  • M. Hochster
  • Mathematics
    Canadian Journal of Mathematics
  • 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
...
1
2
3
4
5
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