What question did this study set out to answer?

To characterize triangular derivations in Noetherian UFDs based on their kernels' structure and generation.

May 6, 2026International Journal of Algebra and Computation0 citations

On certain classes of triangular derivations of R X, Y, Z with three-generated kernels

PDProsenjit Das SLSwapnil A. Lokhande SSSanjay Singha

Key Points

To characterize triangular derivations in Noetherian UFDs based on their kernels' structure and generation.
Analyzed triangular derivations under specific conditions in Noetherian unique factorization domains (UFDs).
Examined generation limits of kernels and relationships between elements of derivations.
Investigated types of elementary and triangular monomial derivations.
The study finds certain triangular derivations have kernels generated by at most three elements.
Identified specific conditions under which these structures hold true.

Abstract

Let Formula: see text be a Noetherian UFD containing Formula: see text and Formula: see text. We show that, under certain conditions, the kernel of the following type of Formula: see text-derivations Formula: see text of Formula: see text is generated by at most Formula: see text elements over Formula: see text: a) Formula: see text is an extension of an Formula: see text-elementary derivation Formula: see text of Formula: see text such that Formula: see text or Formula: see text is a homogeneous polynomial in Formula: see text and Formula: see text with respect to the standard grading. b) Formula: see text is a nice Formula: see text-derivation satisfying Formula: see text and Formula: see text form a regular sequence or are comaximal in Formula: see text. c) Formula: see text is triangular monomial. d) Formula: see text is an extension of an irreducible triangular Formula: see text-derivation Formula: see text of Formula: see text such that Formula: see text.

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