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-14 nucleus is converted into a proton, which increases the atomic number by one, creating nitrogen-14 while emitting a beta particle (which is an electron, denoted as \(0^{-1}\text{e}\)).