Displaying similar documents to “Recent progress on Hilbert's Fourteenth Problem via triangular derivations”

The fourteenth problem of Hilbert for polynomial derivations

Andrzej Nowicki (2002)

Banach Center Publications

Similarity:

We present some facts, observations and remarks concerning the problem of finiteness of the rings of constants for derivations of polynomial rings over a commutative ring k containing the field ℚ of rational numbers.

Some results of reverse derivation on prime and semiprime Γ-rings

Neshtiman Nooraldeen Suliman (2015)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

In the present paper, it is introduced the definition of a reverse derivation on a Γ-ring M. It is shown that a mapping derivation on a semiprime Γ-ring M is central if and only if it is reverse derivation. Also it is shown that M is commutative if for all a,b ∈ I (I is an ideal of M) satisfying d(a) ∈ Z(M), and d(a ∘ b) = 0.

On the Range and the Kernel of Derivations

Bouali, Said, Bouhafsi, Youssef (2006)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30. Let H be a separable infinite dimensional complex Hilbert space and let L(H) denote the algebra of all bounded linear operators on H into itself. Given A ∈ L(H), the derivation δA : L(H)→ L(H) is defined by δA(X) = AX-XA. In this paper we prove that if A is an n-multicyclic hyponormal operator and T is hyponormal such that AT = TA, then || δA(X)+T|| ≥ ||T|| for all X ∈ L(H). We establish the...

On derivations of quantales

Qimei Xiao, Wenjun Liu (2016)

Open Mathematics

Similarity:

A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation. ...

A note on characterizations of rings of constants with respect to derivations

Piotr Jędrzejewicz (2004)

Colloquium Mathematicae

Similarity:

Let A be a commutative algebra without zero divisors over a field k. If A is finitely generated over k, then there exist well known characterizations of all k-subalgebras of A which are rings of constants with respect to k-derivations of A. We show that these characterizations are not valid in the case when the algebra A is not finitely generated over k.