  This paper introduces a class of rings called left nil zero semicommutative
rings ( LNZS rings ), wherein a ring R is said to be LNZS if the left
annihilator of every nilpotent element of R is an ideal of R. It is observed
that reduced rings are LNZS but not the other way around. So, this paper
provides some conditions for an LNZS ring to be reduced, and among other
results, it is proved that R is reduced if and only if the ring of upper
triangular matrices of order 2x2 over R is LNZS. Furthermore, it is shown
through examples that neither the polynomial ring nor the skew polynomial ring
over an LNZS is LNZS. Therefore, this paper investigates the LNZS property of
the polynomial extension and skew polynomial extension of an LNZS ring with
some additional conditions.
