2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33075Using a new definition of generalized divisors we prove that the lattice of such divisors for a given linear partial differential operator is modular and obtain analogues of the well-known theorems of the Loewy-Ore theory of factorization of linear ordinary differential operators. Possible applications to factorized Groebner bases computations in the commutative and non-commutative cases are discussed, an application to finding criterions of Darboux integrability of nonlinear PDEs is given.LaTeX 2.09, acmconf.sty (included in the tar file), 8 pages. Presented at the Poster session of ISSAC'98 (Rostock, Germany)Symbolic ComputationExactly Solvable and Integrable SystemsI.1text