Minimal coverings in the Rogers semilattices of $\Sigma_n^0$-computable numberings

Under study is the problem of existence of minimal and strong minimal coverings in Rogers semilattices of $\Sigma_n^0$-computable numberings for $n\ge 2$. Two sufficient conditions for existence of minimal coverings and one sufficient condition for existence of strong minimal coverings are found. The problem is completely solved of existence of minimal coverings in Rogers semilattices of $\sum_n^0$-computable numberings of a finite family.