Spectral Ideals and Spectral Subalgebras of an Algebra
Spectral Real Semigroups
The notion of a real semigroup was introduced in [8] to provide a framework for the investigation of the theory of (diagonal) quadratic forms over commutative, unitary, semi-real rings. In this paper we introduce and study an outstanding class of such structures, that we call spectral real semigroups (SRS). Our main results are: (i) The existence of a natural functorial duality between the category of SRSs and that of hereditarily normal spectral spaces; (ii) Characterization of the SRSs as the...
Spectrally arbitrary tree sign patterns of order 4.
Spectre irréductible d'un module.
Spezielle Algebren und transitive Operationen.
Squarefree monomial ideals with maximal depth
Let be a Noetherian local ring and a finitely generated -module. We say has maximal depth if there is an associated prime of such that depth . In this paper we study squarefree monomial ideals which have maximal depth. Edge ideals of cycle graphs, transversal polymatroidal ideals and high powers of connected bipartite graphs with this property are classified.
Stabilisation de la -théorie algébrique des espaces topologiques
Stability, duality, 2-generated ideals and a canonical decomposition of modules
Stability of algebraic inverse systems, I: Stability, weak stability and the weakly-stable socle
Stability of some integral domains on a pullback
Stability of Two-Dimensional Local Rings. I.
Stability Theorems for Overrings of Polynomial Rings.
Stable Reduction and Uniformization of Abelian Varieties I.
Stable reduction and uniformization of abelian varieties II.
Stable short exact sequences and the maximal exact structure of an additive category
It was recently proved that every additive category has a unique maximal exact structure, while it remained open whether the distinguished short exact sequences of this canonical exact structure coincide with the stable short exact sequences. The question is answered by a counterexample which shows that none of the steps to construct the maximal exact structure can be dropped.
Standard monmials of some symmetric sets.
Standard monomials for q-uniform families and a conjecture of Babai and Frankl
Let n, k, α be integers, n, α>0, p be a prime and q=p α. Consider the complete q-uniform family We study certain inclusion matrices attached to F(k,q) over the field . We show that if l≤q−1 and 2l≤n then This extends a theorem of Frankl [7] obtained for the case α=1. In the proof we use arguments involving Gröbner bases, standard monomials and reduction. As an application, we solve a problem of Babai and Frankl related to the size of some L-intersecting families modulo q.
Standard systems of parameters and their blowing-up rings.
Standard threads and distributivity.
Stanley decompositions and polarization
We define nice partitions of the multicomplex associated with a Stanley ideal. As the main result we show that if the monomial ideal is a CM Stanley ideal, then is a Stanley ideal as well, where is the polarization of .