Abstract:
In this article the structure of the lattice of closed classes of polynomials
modulo $k$ is investigated. More precisely, we investigate the structure
of the interval of this lattice from the class of all linear polynomials
with zero constant term to the class of all polynomials modulo $k$.
It is proved that this interval (as partially ordered set) is the
direct product of two subintervals, and its structure is completely
determined when $k$ is square free. Moreover, for $k=4$ (minimal
not square free $k$) the description of the interval from the class
of all linear polynomials to the class of all polynomials is given.
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