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Let $D$ be an integral domain with the quotient field $K$ , $X$ an indeterminate over $K$ and $x$ an element of $D$ . The Bhargava ring over $D$ at $x$ is defined to be $𝔹_{x} (D) : = {f \in K [X] : for all a \in D, f (x X + a) \in D [X]}$ . In fact, $𝔹_{x} (D)$ is a subring of the ring of integer-valued polynomials over $D$ . In this paper, we aim to investigate the behavior of $𝔹_{x} (D)$ under localization. In particular, we prove that $𝔹_{x} (D)$ behaves well under localization at prime ideals of $D$ , when $D$ is a locally finite intersection of localizations. We also attempt a classification of integral domains $D$ ...

On chains of centered valuations.

Chibloun, Rachid (2003)

International Journal of Mathematics and Mathematical Sciences

On constructing resolutions over the polynomial algebras.

Johansson, Leif, Lambe, Larry, Sköldberg, Emil (2002)

Homology, Homotopy and Applications

On generating sets of minimal length for polynomial ideals

BODO RENSCHUCH, Henrik Bresinsky (1987)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

On local derivations in the Kadison sense

Andrzej Nowicki (2001)

Colloquium Mathematicae

Let k be a field. We prove that any polynomial ring over k is a Kadison algebra if and only if k is infinite. Moreover, we present some new examples of Kadison algebras and examples of algebras which are not Kadison algebras.

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O čtrnáctém Hilbertově problému

On $A^{1}$ -fibrations of subalgebras of polynomial algebras

On a formula of Beniamino Segre.

On A Problem Of Samuel

On a theorem by Kronecker.

On a theorem of F. S. Macaulay on colon ideals.

On Bhargava rings

On chains of centered valuations.

On constructing resolutions over the polynomial algebras.

On generating sets of minimal length for polynomial ideals

On local derivations in the Kadison sense

On Polynomials and Exponential Polynomials in Several Complex Variables.

On polynomials whose fibres are irreducible with no critical points.

On Prüfer domains of polynomials.

On radical-equivalent and zero-equivalent ideals

On some generalizations of Jacobi's residue formula

On some partial orders associated to generic initial ideals.

On some properties of polynomial rings.

On standard basis and multiplicity of $(X^{a} - Y^{b}, X^{c} - Y^{d})$ .

On Stanley-Reisner rings

Currently displaying 1 – 20 of 48