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Suppose that R is a ring with unity 1 and a is an element

Chapter 12, Problem 39E

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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?

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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.

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