2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120068We study algebraic properties of matrices whose rows are mutual neighbours, and are also neigbours of 0 ("neighbour" in the sense of a certain nilpotency condition). The intended application is in synthetic differential geometry. For a square matrix of this kind, the product of the diagonal entries equals the determinant, modulo a factor n!Rings and AlgebrasDifferential Geometry15A33, 51K10text