Hereditary ring
= Hereditary ring
A <ring> is left hereditary if every submodule of a left <projective module> is projective. Equivalently, every left <module> has a <projective resolution> of length at most one. The <standard projective resolution of a quiver representation>, used also for arbitrary infinite-dimensional <modules>, proves that <path algebras> of finite <quivers> over a <field> are left hereditary.