A note on the dual of a finitely generated multiplication module
A note on the one-dimensional systems of formal equations
On this paper we compute the numerical function of the approximation theorem of M. Artin for the one-dimensional systems of formal equations.
A procedure to compute prime filtration
Let K be a field, S = K[x 1, … x n] be a polynomial ring in n variables over K and I ⊂ S be an ideal. We give a procedure to compute a prime filtration of S/I. We proceed as in the classical case by constructing an ascending chain of ideals of S starting from I and ending at S. The procedure of this paper is developed and has been implemented in the computer algebra system Singular.
A remark on Hodge algebras and Gröbner bases
A Remark on Rings with Primary Ideals as Maximal Ideals.
A remark on the quadratic analogue of the Quillen-Suslin theorem.
A short proof of a fibre criterion for polynomials to belong to an ideal.
A simple characterization of principal ideal domains
1. Introduction. In this note we give necessary and sufficient conditions for an integral domain to be a principal ideal domain. Curiously, these conditions are similar to those that characterize Euclidean domains. In Section 2 we establish notation, discuss related results and prove our theorem. Finally, in Section 3 we give two nontrivial applications to real quadratic number fields.
A simple proof of uniqueness for torsion modules over principal ideal domains.
The aim of this note is to give an alternative proof of uniqueness for the decomposition of a finitely generated torsion module over a P.I.D. (= principal ideal domain) as a direct sum of indecomposable submodules.Our proof tries to mimic as far as we can the standard procedures used when dealing with vector spaces.For the sake of completeness we also include a proof of the existence theorem.
A strong complement property of Dedekind domains
A structure theorem for sets of lengths
A survey on local cohomology and 𝓓-modules
A theory of multiplicity for multiplictive filtrations.
A “-operation free” approach to Prüfer -multiplication domains.
A weakening of the euclidean property for integral domains and applications to algebraic number theory. II.
A weakening of the euclidean property for integral domains and applications to algebraic number theory. I.
Abelian Groups with an Endomorphism with Irreducible minimum Polynomial
Abelsche Galoiserweiterungen von R[X].
About the Witt rings of function fields of algebroid quadratic quasihomogeneous surfaces.
Absolutely S-domains and pseudo-polynomial rings
A domain R is called an absolutely S-domain (for short, AS-domain) if each domain T such that R ⊆ T ⊆ qf(R) is an S-domain. We show that R is an AS-domain if and only if for each valuation overring V of R and each height one prime ideal q of V, the extension R/(q ∩ R) ⊆ V/q is algebraic. A Noetherian domain R is an AS-domain if and only if dim (R) ≤ 1. In Section 2, we study a class of R-subalgebras of R[X] which share many spectral properties with the polynomial ring R[X] and which we call pseudo-polynomial...