Relations To Other Properties of Rings
- Annihilators are used to define left Rickart rings and Baer rings.
- The set of (left) zero divisors DS of S can be written as
(Here we allow zero to be a zero divisor.)
- In particular DS is the set of (left) zero divisors of R when S = R and R acts on itself as a left R-module.
- When R is commutative, the set DR is precisely equal to the union of the minimal prime ideals of R.
Read more about this topic: Annihilator (ring Theory)
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