منابع مشابه
Endomorphisms of Polynomial Rings ; the Jacobian Conjecture
The Jacobian Conjecture is established : If f1, · · · , fn be elements in a polynomial ring k[X1, · · · , Xn] over a field k of characteristic zero such that det(∂fi/∂Xj) is a nonzero constant, then k[f1, · · · , fn] = k[X1, · · · , Xn]. Let k be an algebraically closed field, let k be an affine space of dimension n over k and let f : k −→ k be a morphism of algebraic varieties. Then f is given...
متن کاملEndomorphisms of Polynomial Rings with Invertible Jacobians
The Jacobian Conjecture is established : Let T be a polynomial ring over a field k of characteristic zero in finitely may variables. Let S be a k-subalgebra of T such that T is unramified over S. Then T = S. Let k be an algebraically closed field, let k be an affine space of dimension n over k and let f : k −→ k be a morphism of algebraic varieties. Then f is given by coordinate functions f1, ....
متن کاملEndomorphisms of Polynomial Rings and Jacobians
The Jacobian Conjecture is established : If f1, · · · , fn be elements in a polynomial ring k[X1, · · · , Xn] over a field k of characteristic zero such that det(∂fi/∂Xj) is a nonzero constant, then k[f1, · · · , fn] = k[X1, · · · , Xn]. Let k be an algebraically closed field, let k be an affine space of dimension n over k and let f : k −→ k be a morphism of algebraic varieties. Then f is given...
متن کاملPolynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms
We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups. The proof uses algebraic self-maps of affine spaces over finite fields. In particular, we prove that when such a map is dominant, the set of its fixed closed scheme points is Zariski dense in the af...
متن کاملLocally finite basic classical simple Lie superalgebras
In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2007
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2007.02.005