  The Compute-and-Forward protocol in quasi-static channels normally employs
lattice codes based on the rational integers $\mathbb{Z}$, Gaussian integers
$\mathbb{Z}\left[i\right]$ or Eisenstein integers
$\mathbb{Z}\left[\omega\right]$, while its extension to more general channels
often assumes channel state information at transmitters (CSIT). In this paper,
we propose a novel scheme for Compute-and-Forward in block-fading channels
without CSIT, which is referred to as Ring Compute-and-Forward because the
fading coefficients are quantized to the canonical embedding of a ring of
algebraic integers. Thanks to the multiplicative closure of the algebraic
lattices employed, a relay is able to decode an algebraic-integer linear
combination of lattice codewords. We analyze its achievable computation rates
and show it outperforms conventional Compute-and-Forward based on
$\mathbb{Z}$-lattices. By investigating the effect of Diophantine approximation
by algebraic conjugates, we prove that the degrees-of-freedom (DoF) of the
optimized computation rate is ${n}/{L}$, where $n$ is the number of blocks and
$L$ is the number of users.
