Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes.
In this paper we compute the Poincaré-Hodge polynomial of a symmetric product of a compact kähler manifold, following the method used by Macdonald, in the topological case, to compute the Poincaré polynomial of a compact polyhedron, and we give some applications, in particular to the case of curves.
We investigate the elasticity of atomic domains of the form ℜ = A + XB[X], where X is an indeterminate, A is a local domain that is not a field, and A ⊂ B is a minimal extension of integral domains. We provide the exact value of the elasticity of ℜ in all cases depending the position of the maximal ideals of B. Then we investigate when such domains are half-factorial domains.
For an atomic domain , its elasticity is defined by : for irreducible . We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants defined by : for irreducible . As a main result we characterize all orders in algebraic number fields having finite elasticity. On the way, we obtain a series of results concerning the invariants and for monoids and integral domains which are of independent interest.
The paper deals with realizations of R-algebras A as endomorphism algebras End G ≅ A of suitable R-modules G over a commutative ring R. We are mainly interested in the case of R having "many prime ideals", such as R = ℝ[x], the ring of real polynomials, or R a non-discrete valuation domain