  In this article the reduction of a $n$-dimensional space to a $k$-dimensional
space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$
stands for the number of single-particle states per unit of spatial length. It
turns out, this space reduction could be understood as another definition of
inflation. It is shown that the introduction of the non-associativity of the
algebra of physical fields in a homogeneous space leads to a nonlinear
equation, the solutions of which can be considered as two-stage inflation.
Using the example of reduction $T\times R^7$ to $T\times R^3$, it is shown that
there is a continuous cross-linking of the Friedmann and inflationary stages of
algebraic inflation at times $10^{-15}$ with the number of baryons $10^{80}$ in
the Universe. In this paper, we construct a new gravitational constant based on
a nonassociative octonion algebra.
