10 citations · 13 across the 4 of their papers we have counts for
5 papers
Rank and rigidity of locally nilpotent derivations of affine fibrations
Janaki Raman Babu, Prosenjit Das, Swapnil A. Lokhande
In this exposition, we propose a notion of rank and rigidity of locally nilpotent derivations of affine fibrations. We show that the concept is analogous to the perception of rank…
NP-Completeness Results for Graph Burning on Geometric Graphs
Arya Tanmay Gupta, Swapnil A. Lokhande, Kaushik Mondal
Graph burning runs on discrete time steps. The aim is to burn all the vertices in a given graph in the least number of time steps. This number is known to be the burning number of…
Some K-theoretic properties of the kernel of a locally nilpotent derivation on k[X_1, \dots, X_4]
S. M. Bhatwadekar, Neena Gupta, Swapnil A. Lokhande
Let k be an algebraically closed field of characteristic zero, D a locally nilpotent derivation on the polynomial ring k[X_1, X_2,X_3,X_4] and A the kernel of D. A question of M. M…
Projective modules over overrings of polynomial rings and a question of Quillen
M. K. Keshari, Swapnil A. Lokhande
Let $(R,\mm,K)$ be a regular local ring containing a field such that either char or char and tr-deg $K/\BF_p\geq 1$. Let be regular parameters of $…
A note on rigidity and triangulability of a derivation
Manoj K. Keshari, Swapnil A. Lokhande
Let A be a -domain, K=frac(A), B=A^{[n]} and D\in \lnd_A(B). Assume rank D= rank D_K=r, where D_K is the extension of D to K^{[n]}. Then we show that (i) If D_K is rig…