Does hereditary and connected imply that the underlying ring $k$ of a $k$-algebra is a field?

All rings are assumed to be associative and have a 1. Let $k$ be a commutative artininan ring and $R$ a finitely generated $k$-algebra. Is it true that if $R$ is connected and hereditary, then $k$ is a field?

EDIT: As pointed out by YCor and Benjamin Steinberg, we must also require $k$ to be faithfully embedded in the center of $R$.