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:
“I want relations which are not purely personal, based on purely personal qualities; but relations based upon some unanimous accord in truth or belief, and a harmony of purpose, rather than of personality. I am weary of personality.... Let us be easy and impersonal, not forever fingering over our own souls, and the souls of our acquaintances, but trying to create a new life, a new common life, a new complete tree of life from the roots that are within us.”
—D.H. (David Herbert)
“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)
“We will have rings and things, and fine array,
And kiss me, Kate, we will be married o’ Sunday.”
—William Shakespeare (1564–1616)