arXiv subjects

Ivana Varga

Publications and source records attributed to Ivana Varga.

2 recordsLinked to original sources

arXiv2026

Expansions of the group $Z_8$ (Part I)

We investigate clones in the interval between the group polynomials and the ring polynomials of ${\mathbb Z}_8$. This is the simplest open case of the problem, as the answer is known for ${\mathbb Z}_{p^2}$ (with $p$ prime) and, in general, ${\mathbb Z}_n$ reduces to the case when $n$ is a prime power. The investigated structure proves to be very complicated, so we provide only a partial description. We restrict our attention to polynomials whose nonlinear monomials have even coefficients.

math.LO↗

arXiv2020

Clones of Compatible Operations on Rings Z_{p^k}}

We investigate the lattice I(n) of clones on the ring Z_n between the clone of polynomial functions and the clone of congruence preserving functions. The crucial case is when n is a prime power. For a prime p, the lattice I(p) is trivial and I(p^2) is known to be a 2-element lattice. We provide a description of I(p^3). To achieve this result, we prove a reduction theorem, which says that I(p^k) is isomorphic to a certain interval in the lattice of clones on Z_p^(k-1).

math.RA↗