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Algebras with finitely generated invariant subalgebras

Ivan V. Arzhantsev (2003)

Annales de l’institut Fourier

We classify all finitely generated integral algebras with a rational action of a reductive group such that any invariant subalgebra is finitely generated. Some results on affine embeddings of homogeneous spaces are also given.

Almost Prüfer v-multiplication domains and the ring D + X D S [ X ]

Qing Li (2010)

Colloquium Mathematicae

This paper is a continuation of the investigation of almost Prüfer v-multiplication domains (APVMDs) begun by Li [Algebra Colloq., to appear]. We show that an integral domain D is an APVMD if and only if D is a locally APVMD and D is well behaved. We also prove that D is an APVMD if and only if the integral closure D̅ of D is a PVMD, D ⊆ D̅ is a root extension and D is t-linked under D̅. We introduce the notion of an almost t-splitting set. D ( S ) denotes the ring D + X D S [ X ] , where S is a multiplicatively closed...

Almost Q -rings

C. Jayaram (2004)

Archivum Mathematicum

In this paper we establish some new characterizations for Q -rings and Noetherian Q -rings.

Almost π -lattices

C. Jayaram (2004)

Czechoslovak Mathematical Journal

In this paper we establish some conditions for an almost π -domain to be a π -domain. Next π -lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for π -rings.

An algorithm to compute the kernel of a derivation up to a certain degree

Stefan Maubach (2001)

Annales Polonici Mathematici

An algorithm is described which computes generators of the kernel of derivations on k[X₁,...,Xₙ] up to a previously given bound. For w-homogeneous derivations it is shown that if the algorithm computes a generating set for the kernel then this set is minimal.

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