Displaying similar documents to “Length 2 variables of A[x,y] and transfer”

Stable elements of Banach and Fréchet algebras

Graham Allan (1998)

Studia Mathematica

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We introduce an algebraic notion-stability-for an element of a commutative ring. It is shown that the stable elements of Banach algebras, and of Fréchet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a purely algebraic nature. This approach leads to other natural questions.

On the stable equivalence problem for k[x,y]

Robert Dryło (2011)

Colloquium Mathematicae

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L. Makar-Limanov, P. van Rossum, V. Shpilrain and J.-T. Yu solved the stable equivalence problem for the polynomial ring k[x,y] when k is a field of characteristic 0. In this note we give an affirmative solution for an arbitrary field k.

Polynomial systems theory applied to the analysis and design of multidimensional systems

Jari Hatonen, Raimo Ylinen (2003)

International Journal of Applied Mathematics and Computer Science

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The use of a principal ideal domain structure for the analysis and design of multidimensional systems is discussed. As a first step it is shown that a lattice structure can be introduced for IO-relations generated by polynomial matrices in a signal space X (an Abelian group). It is assumed that the matrices take values in a polynomial ring F[p] where F is a field such that F[p] is a commutative subring of the ring of endomorphisms of X. After that it is analysed when a given F[p] acting...

Around stable forking

Byunghan Kim, A. Pillay (2001)

Fundamenta Mathematicae

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We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory T has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.