- #1
SMA_01
- 218
- 0
Showing a subset is a subring?
Let R be a ring and a a fixed element in R. Let Ia={x in R l ax=0}
I saw these conditions in my book, but I'm not sure are these conditions sufficient in showing Ia is a subring?
(1) 0 is in Ia:
Let 0 be in R, then
a(0)=0
(2) (a-b)is in Ia, for a, b in Ia:
I'm not sure how I should start this.
(3) Ia is closed under multipication.
Homework Statement
Let R be a ring and a a fixed element in R. Let Ia={x in R l ax=0}
Homework Equations
The Attempt at a Solution
I saw these conditions in my book, but I'm not sure are these conditions sufficient in showing Ia is a subring?
(1) 0 is in Ia:
Let 0 be in R, then
a(0)=0
(2) (a-b)is in Ia, for a, b in Ia:
I'm not sure how I should start this.
(3) Ia is closed under multipication.