Kernel of locally nilpotent 𝑅-derivations of 𝑅[𝑋,𝑌]

DOI10.1090/S0002-9947-97-01946-6zbMath0883.13006OpenAlexW1664503166MaRDI QIDQ4372546

Amartya K. Dutta, Shrikaut M. Bhatwadekar

Publication date: 16 December 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-01946-6

zbMATH Keywords

polynomial ringlocally nilpotent derivationsgraded algebrasymbolic Rees algebra

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Graded rings (13A02) Morphisms of commutative rings (13B10) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (18)

A triviality criterion for \(\mathbb{A}^2\)-fibrations over a ring containing \(\mathbb{Q}\) ⋮ Fixed point free locally nilpotent derivations of \(\mathbb A^2\)-fibrations ⋮ Nice derivations over principal ideal domains ⋮ On finite generation of kernels of locally nilpotent \(R\)-derivations of \(R[X,Y,Z\)] ⋮ Derivations of \(R[X,Y,Z\) with a slice] ⋮ Structure of the kernel of a locally nilpotent derivation on an affine normal domain ⋮ A criterion to determine residual coordinates of \(\mathbb{A}^{2}\)-fibrations ⋮ ON SEPARABLE AND -FORMS ⋮ Some results on retracts of polynomial rings ⋮ Triangulable locally nilpotent derivations in dimension three ⋮ Infinitely generated Derksen and Makar-Limanov invariant ⋮ Some patching results on algebras over two-dimensional factorial domains ⋮ Derivations having divergence zero on \(R[X,Y\).] ⋮ Locally nilpotent derivations of factorial domains ⋮ Structure of \(\mathbb{A}^2\)-fibrations having fixed point free locally nilpotent derivations ⋮ Class group of the ring of invariants of an exponential map on an affine normal domain ⋮ On algebras which are locally 𝔸¹ in codimension-one ⋮ Coordinates ofR[x,y: Constructions and Classifications]

Cites Work

• On a problem of Zariski
• Krull dimension, transcendence degree and subalgebras of finitely generated algebras
• Locally polynomial algebras are symmetric algebras
• On finding and cancelling variables in k[X,Y,Z]
• Locally nilpotent derivations over a UFD and an application to rank two locally nilpotent derivations of \(k[X_1,\dots,X_n\)]
• Introduction to Grothendieck duality theory
• On the uniqueness of the coefficient ring in a polynomial ring
• On residual variables and stably polynomial algebras
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