On radical-equivalent and zero-equivalent ideals
On Rank 4 Quadratic Spaces with Given Arf and Witt Invariants.
On Rao's theorems and the Lazarsfeld-Rao property
On reconstructing algebraic sets and ideals
We generalize some results on reconstructing sets to the case of ideals of 𝕜[X₁,...,Xₙ]. We show that reconstructing sets can be approximated by finite subsets having the property of reconstructing automorphisms of bounded degree.
On reconstruction of polynomial automorphisms
We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.
On reflexivity of representations of local Commutative Algebras
On relations of invariants for vector-valued forms.
On relative real holomorphy rings.
On ring derivations and quadratic functionals.
On ring theoretic lattice modules
On Rings admitting orderings and 2-primary chains of orderings of higher level.
On rings of constants of derivations in two variables in positive characteristic
Let k be a field of chracteristic p > 0. We describe all derivations of the polynomial algebra k[x,y], homogeneous with respect to a given weight vector, in particular all monomial derivations, with the ring of constants of the form , where .
On roots of polynomials with power series coefficients
We give a deepened version of a lemma of Gabrielov and then use it to prove the following fact: if h ∈ 𝕂[[X]] (𝕂 = ℝ or ℂ) is a root of a non-zero polynomial with convergent power series coefficients, then h is convergent.
On ruled fields
Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.
On semicontinuity of ramification invariants in dimension 2.
On seminormal schemes
On Separable Subalgebras of Azumaya Algebras
On soluble groups of module automorphisms of finite rank
Let be a commutative ring, an -module and a group of -automorphisms of , usually with some sort of rank restriction on . We study the transfer of hypotheses between and such as Noetherian or having finite composition length. In this we extend recent work of Dixon, Kurdachenko and Otal and of Kurdachenko, Subbotin and Chupordia. For example, suppose is -Noetherian. If has finite rank, then also is -Noetherian. Further, if is -Noetherian and if only certain abelian sections...
On some algebraic and geometric extension of the theory of adjoints
On some class groups of an integral domain