The epimorphism theorem and its generalizations (Q2947373)

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scientific article

Language	Label	Description	Also known as
English	The epimorphism theorem and its generalizations	scientific article

Statements

scholarly article

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The epimorphism theorem and its generalizations (English)

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Amartya K. Dutta

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publication date

22 September 2015

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zbMATH Keywords

polynomial rings

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epimorphism theorem

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embedding problem

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affine fibrations

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cancellation problem

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linearization problem

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MaRDI profile type

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On the uniqueness of the coefficient ring in a polynomial ring

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Geometric theory of algebraic space curves

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Embeddings of Certain Curves in the Affine Plane

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Uniqueness of plane embeddings of special curves

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Polynomial fibre rings of algebras over noetherian rings

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Non-linearizable algebraic group actions on \(\mathbb{A}^ n\)

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Structure of \(\mathbb A^2\)-fibrations over one-dimensional Noetherian domains

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Non-linearizable algebraic \(k^*\)-actions on affine spaces

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Locally polynomial algebras are symmetric algebras

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Generalized epimorphism theorem

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Some results on embedding of a line in 3-space

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On residual variables and stably polynomial algebras

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Linear planes over a discrete valuation ring

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On algebras which are locally 𝔸¹ in codimension-one

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A note on the cancellation property of k[X, Y]

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An algebraic proof of a cancellation theorem for surfaces

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A Note on Locally Nilpotent Derivations and Variables of <i>k</i>[<i>X</i>, <i>Y</i>, <i>Z</i>]

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Triangular derivations of \({\mathbf k}[X_1,X_2,X_3,X_4]\)

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Families of Affine Fibrations

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On codimension-one \(\mathbb A^1\)-fibration with retraction

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Planes of the form \(b(X,Y)Z^n-a(X,Y)\) over a DVR

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Nonlinearizable holomorphic group actions

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On \(\mathbb{A}^ 1\)-bundles of affine morphisms

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Non straightenable complex lines in \(\mathbb C^2\)

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On Zariski problem

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A note on seminormal rings and \({\mathbb{A}}^ 1\)-fibrations

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On the cancellation problem for the affine space \(\mathbb{A}^{3}\) in characteristic \(p\)

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On the family of affine threefolds

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On Zariski's cancellation problem in positive characteristic

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On contractible curves in the complex affine plane

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A new proof of the Abhyankar-Moh-Suzuki theorem

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A topological proof of cancellation theorem for \(\mathbb{C}^2\). (With an appendix written in collaboration with C. R. Pradeep)

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On the \(R\)-invariance of \(R[X]\)

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The extension of regular and rational embeddings

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ℂ*-actions on ℂ³ are linearizable

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Polynomials with general \(\mathbb{C}^ 2\)-fibers are variables.

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Simple birational extensions of the polynomial algebra ℂ^{[3]}

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On Abhyankar-Moh's Epimorphism Theorem

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Vénéreau-type polynomials as potential counterexamples

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On the hypersurface \(x+x^2y+z^2+t^3=0\) in \(\mathbb{C}^4\) or a \(\mathbb{C}^3\)-like threefold which is not \(\mathbb{C}^3\)

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A new proof of the Abhyankar–Moh–Suzuki theorem via a new algorithm for the polynomial dependence

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An algebraic characterization of the affine plane

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Affine surfaces containing cylinderlike open sets

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Complete intersections

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Abhyankar-Sathaye Embedding Conjecture for a geometric case

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A topological characterisation of the affine plane as an algebraic variety

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On the computation of minimal polynomials

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On finding and cancelling variables in k[X,Y,Z]

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Hamburger-Noether expansions and approximate roots of polynomials

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On affine-ruled rational surfaces

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Generalized Newton-Puiseux expansion and Abhyankar-Moh semigroup theorem

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Polynomial ring in two variables over a D.V.R.: A criterion

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Polynomial representations of knots

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On the embedding dimension of an affine variety

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Propriétés topologiques des polynômes de deux variables complexes et automorphismes algébriques de l'espace \(C^2\)

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Hyperplanes of the Form <i>f</i>1(<i>x</i>, <i>y</i>)<i>z</i><sub>1</sub> + · · · + <i>f<sub>k</sub></i>(<i>x</i>, <i>y</i>)<i>z<sub>k</sub></i> + <i>g</i>(<i>x</i>, <i>y</i>) Are Variables

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Cancellation of variables of the form \(bT^n-a\)

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Projective algebras

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A new topological proof of the Abhyankar-Moh theorem

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full work available at URL

https://doi.org/10.1142/s0219498815400101

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Journal of Algebra and its Applications

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Identifiers

zbMATH Open document ID

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10.1142/S0219498815400101

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2947373

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