Solution Found!
Suppose that R is a ring with unity 1 and a is an element
Chapter 12, Problem 39E(choose chapter or problem)
QUESTION:
Problem 39E
Suppose that R is a ring with unity 1 and a is an element of R such that a2 = 1. Let S = {ara | r ∈ R}. Prove that S is a subring of R. Does S contain 1?
Questions & Answers
QUESTION:
Problem 39E
Suppose that R is a ring with unity 1 and a is an element of R such that a2 = 1. Let S = {ara | r ∈ R}. Prove that S is a subring of R. Does S contain 1?
ANSWER:
Step 1 of 5
As per the definition of the ring, a ring is a set which have two binary operations that are, addition and multiplication. To prove is a subring of , and as per the definition of subring, a set is subring of if it satisfies the operations of . So, apply subring test to prove that is a subring.