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 .
Stanley decompositions of the Bracket ring.
Stanley depth of monomial ideals with small number of generators
For a monomial ideal I ⊂ S = K[x 1...,x n], we show that sdepth(S/I) ≥ n − g(I), where g(I) is the number of the minimal monomial generators of I. If I =νI′, where ν ∈ S is a monomial, then we see that sdepth(S/I) = sdepth(S/I′). We prove that if I is a monomial ideal I ⊂ S minimally generated by three monomials, then I and S/I satisfy the Stanley conjecture. Given a saturated monomial ideal I ⊂ K[x 1,x 2,x 3] we show that sdepth(I) = 2. As a consequence, sdepth(I) ≥ sdepth(K[x 1,x 2,x 3]//I) +1...
Stanley filtrations and strongly stable ideals.