Show that the subset S = {0,2,4,6,8} of Z10 is a subring. Does S have identity?

Gretchen Allison

Gretchen Allison

Answered question

2022-09-05

Show that the subset S = {0,2,4,6,8} of Z10 is a subring. Does S have identity?

Answer & Explanation

Jazmin Bryan

Jazmin Bryan

Beginner2022-09-06Added 12 answers

Notice that S is the set of all elements that may be written as 2k. Let 2k,2j ? S. Then 2k + 2j = 2(k + j) so clearly the sum is in S. Also (2k)(2j) = 4kj = 2(2kj) and the product is in S. We also see that 0, the additive identity for Z10, is in S by de?nition. Finally, if 2k ? S, then ?2k ? S. Therefore S is a subring of Z10. S has an identity, namely 6. We check that 2

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?