Endomorphisms, derivations, and polynomial rings
نویسندگان
چکیده
منابع مشابه
Endomorphisms 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 کاملEndomorphisms 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 کاملOn Endomorphisms of Polynomial Rings with Invertible Jacobians
The Jacobian Conjecture can be generalized and is established : Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with T = k. 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 b...
متن کاملDerivations in semiprime rings and Banach algebras
Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,yin R$ where $0neq bin R$, then there exists a central idempotent element $e$ of $U$ such that $eU$ is commutative ring and $d$ induce a zero derivation on $(1-e)U$. ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1978
ISSN: 0021-8693
DOI: 10.1016/0021-8693(78)90213-2