  Let f:E-->B be a fibration of fiber F. Eilenberg and Moore have proved that
there is a natural isomorphism of vector spaces between H^*(F;F_p) and
Tor^{C^*(B)}(C^*(E),F_p). Generalizing the rational case proved by Sullivan,
Anick [Hopf algebras up to homotopy, J. Amer. Math. Soc. 2 (1989) 417--453]
proved that if X is a finite r-connected CW-complex of dimension < rp+1 then
the algebra of singular cochains C^*(X;F_p) can be replaced by a commutative
differential graded algebra A(X) with the same cohomology. Therefore if we
suppose that f:E-->B is an inclusion of finite r-connected CW-complexes of
dimension < rp+1, we obtain an isomorphism of vector spaces between the algebra
H^*(F;F_p) and Tor^{A(B)}(A(E),F_p) which has also a natural structure of
algebra. Extending the rational case proved by Grivel-Thomas-Halperin [PP
Grivel, Formes differentielles et suites spectrales, Ann. Inst. Fourier 29
(1979) 17--37] and [S Halperin, Lectures on minimal models, Soc. Math. France
9-10 (1983)] we prove that this isomorphism is in fact an isomorphism of
algebras. In particular, $H^*(F;F_p) is a divided powers algebra and p-th
powers vanish in the reduced cohomology \mathaccent "707E {H}^*(F;F_p).
