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 $$\ge 3$$… Expand

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… Expand

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… Expand

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.… Expand

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,… Expand

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.… Expand