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 to, relations, properties and/or rings:
“I have no wealthy or popular relations to recommend me.”
—Abraham Lincoln (1809–1865)
“So soon did we, wayfarers, begin to learn that man’s life is rounded with the same few facts, the same simple relations everywhere, and it is vain to travel to find it new.”
—Henry David Thoreau (1817–1862)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“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)