2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65399Chas and Sullivan recently defined an intersection product on the homology $H_*(LM)$ of the space of smooth loops in a closed, oriented manifold $M$. In this paper we will use the homotopy theoretic realization of this product described by the first two authors to construct a second quadrant spectral sequence of algebras converging to the loop homology multiplicatively, when $M$ is simply connected. The $E_2$ term of this spectral sequence is $H^*(M;H_*(ΩM))$ where the product is given by the cup product on the cohomology of the manifold $H^* (M)$ with coefficients in the Pontryagin ring structure on the homology of its based loop space $H_*(ΩM)$. We then use this spectral sequence to compute the ring structures of $H_* (LS^n)$ and $H_* (L\bcp^n)$.15 pages, 0 figures, to appear in Proc. of Alg. Topology, Conf., Isle of Skye, 2001Algebraic Topology55T99; 57T99; 58D15text