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)
Famous quotes containing the words relations, properties and/or rings:
“The interest in life does not lie in what people do, nor even in their relations to each other, but largely in the power to communicate with a third party, antagonistic, enigmatic, yet perhaps persuadable, which one may call life in general.”
—Virginia Woolf (1882–1941)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“Ah, Christ, I love you rings to the wild sky
And I must think a little of the past:
When I was ten I told a stinking lie
That got a black boy whipped....”
—Allen Tate (1899–1979)