The equation \( ^{146}\text{C} \rightarrow ^{147}\text{N} + 0^{-1}\text{e} \) represents beta-minus decay. In this process, a neutron in the carbon-146 nucleus is transformed into a proton, resulting in the formation of nitrogen-147 and the emission of a beta particle (an electron, represented as \( 0^{-1}\text{e} \)).
So, the correct response is beta-minus decay.