Classification of p-adic 6-dimensional filiform Leibniz algebras by solutions of x q = a
M. LadraDepartment of Algebra, University of Santiago de Compostela, 15782, Santiago de Compostela, SpainB. A. OmirovInstitute of Mathematics, National University of Uzbekistan, Do’rmon yo’li str. 29, Tashkent, 100125, UzbekistanU. A. RozikovInstitute of Mathematics, National University of Uzbekistan, Do’rmon yo’li str. 29, Tashkent, 100125, Uzbekistan
ABI
Abstract
Abstract We study the p-adic equation x q = a over the field of p-adic numbers. We construct an algorithm which gives a solvability criteria in the case of q = p m and present a computer program to compute the criteria for any fixed value of m ≤ p − 1. Moreover, using this solvability criteria for q = 2; 3; 4; 5; 6, we classify p-adic 6-dimensional filiform Leibniz algebras.