Rings with central annihilator ideal

چکیده مقاله

In this article, we introduce a new class of ideals of rings which consists of central annihilator ideals and demonstrate how to use such ideals in the general study of the structure of rings. We study rings in which the left (right) annihilator of each element is in its center. In the following, we present the structure of these rings. We also prove a version of Cohen’s Theorem in rings that have a nonzero central annihilator ideal. Next, we show that the theory of primary decomposition of proper ideals in commutative Noetherian rings can be extended to a similar primary decomposition of central annihilator ideals.