2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65583We present a theory for splitting algebras of monic polynomials over rings, and apply the results to symmetric functions, and Galois theory. Our main result is that the ring of invariants of a splitting algebra under the symmetric group almost always is the ring of coefficients.13 pagesCommutative Algebra12F05; 12F10; 13B25; 13A50text