Abstract
We define a particular case of hereditary rings called weak
hereditary rings. A sufficient condition for a weak hereditary be hereditary is given. We investigate the transfer of this notion in homomorphic
image of rings, amalgamated duplication of a ring along a proper ideal,
subring retracts, direct product of rings, and in trivial ring extensions. For
the pullback constructions, we give an example showing that the transfer
does not hold.
