Spectral Spaces

  title={Spectral Spaces},
  author={Max A. Dickmann and Niels Schwartz and Marcus Tressl},
5 Citations
Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings
  • J. Fernando
  • Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
  • 2022
A classical problem in real geometry concerns the representation of positive semidefinite elements of a ring A as sums of squares of elements of A. If A is an excellent ring of dimension $$\ge 3$$
Real Spectrum Versus ℓ-Spectrum via Brumfiel Spectrum
  • F. Wehrung
  • Mathematics
    Algebras and Representation Theory
  • 2021
It is well known that the real spectrum of any commutative unital ring, and the l-spectrum of any Abelian lattice-ordered group with order-unit, are all completely normal spectral spaces. We prove
Alexandroff Topology of Algebras Over an Integral Domain
Let S be an integral domain with field of fractions F and let A be an F -algebra. An S -subalgebra R of A is called S -nice if R is lying over S and the localization of R with respect to $$S
Approximation theorems for spaces of localities
The classical Artin–Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values.


Spectral spaces of countable Abelian lattice-ordered groups
  • F. Wehrung
  • Mathematics
    Transactions of the American Mathematical Society
  • 2018
A compact topological space X is spectral if it is sober (i.e., every irreducible closed set is the closure of a unique singleton) and the compact open subsets of X form a basis of the topology of X,
  • Comm. Algebra
  • 2016
  • 2016
One-tilting classes and modules over commutative rings
Abstract We classify 1-tilting classes over an arbitrary commutative ring. As a consequence, we classify all resolving subcategories of finitely presented modules of projective dimension at most 1.
  • 2014
  • J. Pure Appl. Algebra
  • 2013
  • Comm. Algebra
  • 2013
  • 2013
  • Algebra Universalis
  • 2013
  • 2013