Rings in Which Pure Ideals are Generated by Idempotents.
Rings Whose Modules Have Nice Decompositions.
Rings with a theory of gretest common divisors.
Sekiguchi-Suwa theory revisited
We present an account of the construction by S. Sekiguchi and N. Suwa of a cyclic isogeny of affine smooth group schemes unifying the Kummer and Artin-Schreier-Witt isogenies. We complete the construction over an arbitrary base ring. We extend the statements of some results in a form adapted to a further investigation of the models of the group schemes of roots of unity.
Semigroup of Two Irreducible Algebroid Plane Curves.
Semigroups associated to singular points of plane curves.
Semiprime factorizations in unions of Dedekind domains.
Semirigid GCD Domains.
Separable adel algebras and a presentation of Weil groups.
Shellability and the strong gcd-condition.
Sign-graded posets, unimodality of -polynomials and the Charney-Davis conjecture.
Simple birational extensions of two dimensional affine rational domains
Simple Galois extensions of two-dimensional affine rational domains
Skew-symmetric cluster algebras of finite mutation type
In the famous paper [FZ2] Fomin and Zelevinsky obtained Cartan-Killing type classification of all cluster algebras of finite type, i.e. cluster algebras having only finitely many distinct cluster variables. A wider class of cluster algebras is formed by cluster algebras of finite mutation type which have finitely many exchange matrices (but are allowed to have infinitely many cluster variables). In this paper we classify all cluster algebras of finite mutation type with skew-symmetric exchange matrices....
Solution d'une conjecture de C. Berenstein - A. Yger et invariants de contact à l'infini
Soient un corps commutatif et un idéal de l’anneau des polynômes (éventuellement ). Nous prouvons une conjecture de C. Berenstein - A. Yger qui affirme que pour tout polynôme , élément de la clôture intégrale de l’idéal , on a une représentationoù .
Solving quadratic equations over polynomial rings of characteristic two.
We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A.We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain a finite algorithm for solving a polynomial equation over A when A is F[x1, ..., xN] or F(x1,...
Some algebraic properties of hypergraphs
We consider Stanley-Reisner rings where is the edge ideal associated to some particular classes of hypergraphs. For instance, we consider hypergraphs that are natural generalizations of graphs that are lines and cycles, and for these we compute the Betti numbers. We also generalize some known results about chordal graphs and study a weak form of shellability.
Some cardinal invariants for valuation domains
Some characterizaions of smooth, regular, and complete intersection algebras.
Some Homological properties of commutative semitrivial ring extensions.