On sums of homogeneous locally nilpotent derivations

2012/11/12 by Elena Romaskevich, Romaskevich, Elena
Mathematics · #13N15 #14M25 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #math.AC #math.AG #msc:13N15 #msc:14M25

paper · pdf · doi:10.48550/arxiv.1211.2752

12 pages

arxiv created 2012/11/12 · openalex publication_date 2012/11/12 · arxiv updated 2012/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a commutative associative integrally closed k-algebra without zero divisors effectively graded by a lattice. We obtain a criterion of local nilpotency of the sum of two homogeneous locally nilpotent derivations (LNDs) of fiber type on A in terms of their degrees. The same problem is solved for commutators of two homogeneous LNDs.

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