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Length 2 variables of A[x,y] and transfer

Eric Edo, Stéphane Vénéreau (2001)

Annales Polonici Mathematici

We construct and study length 2 variables of A[x,y] (A is a commutative ring). If A is an integral domain, we determine among these variables those which are tame. If A is a UFD, we prove that these variables are all stably tame. We apply this construction to show that some polynomials of A[x₁,...,xₙ] are variables using transfer.

Linear gradings of polynomial algebras

Piotr Jędrzejewicz (2008)

Open Mathematics

Let k be a field, let G be a finite group. We describe linear G -gradings of the polynomial algebra k[x 1, ..., x m] such that the unit component is a polynomial k-algebra.

Local derivations in polynomial and power series rings

Janusz Zieliński (2002)

Colloquium Mathematicae

We give a description of all local derivations (in the Kadison sense) in the polynomial ring in one variable in characteristic two. Moreover, we describe all local derivations in the power series ring in one variable in any characteristic.

Maximal non-Jaffard subrings of a field.

Mabrouk Ben Nasr, Noôman Jarboui (2000)

Publicacions Matemàtiques

A domain R is called a maximal non-Jaffard subring of a field L if R ⊂ L, R is not a Jaffard domain and each domain T such that R ⊂ T ⊆ L is Jaffard. We show that maximal non-Jaffard subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dimv R = dim R + 1. Further characterizations are given. Maximal non-universally catenarian subrings of their quotient fields are also studied. It is proved that this class of domains coincides with the previous class when R is integrally...

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