2025-08-042025-08-042025-06-27https://repositorio.bc.ufg.br/tede/handle/tede/14564Clifford Algebras are an abstract construct related to bilinear vector spaces, whilst Polynomials with R^4 coefficients are a generalization of the study of polynomials with complex coefficients. The study of tensor product and tensor algebras is first presented as a theoretical base to be build upon. The definition of a Clifford Algebra over the real numbers and its universal property are studied. The classification of Clifford Algebras related to real finite-dimensional vector spaces is presented with the use of the Periodicity Theorem. Then the presentation eight algebras defined in R^4 is done. The classification of roots from one sided polynomials with quartenionic coefficients is first presented, followed by the one-sided polynomials over noncommutative algebras of R^4, and then by the two-sided quaternionic polynomial’s case.Acesso Abertohttp://creativecommons.org/licenses/by-nc-nd/4.0/Álgebras de CliffordClassificação das álgebras reais de CliffordPolinômios com álgebras de R^4Classificação de raízes de polinômiosClifford algebrasClassification of real Clifford algebrasPolynomials with algebras of R^4Classification of polynomials’ rootsCIENCIAS EXATAS E DA TERRA::MATEMATICADissertação