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# Algebra: Which of the following are rings with the usual addition and multiplication?

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1. (a) N0 = N ∪ {0}.
(b) {f(X) ∈ R[X] : f(X) = 0 or deg f(X) ≤ 5}.
(c) {A ∈ M2(R) : det A = 0 or det A = 1}.
(d) {a ∈ Q : a =b/2 for some b ∈ Z}.

Thanks in advance.
2. (Original post by Spiral1977)
(a) N0 = N ∪ {0}.
(b) {f(X) ∈ R[X] : f(X) = 0 or deg f(X) ≤ 5}.
(c) {A ∈ M2(R) : det A = 0 or det A = 1}.
(d) {a ∈ Q : a =b/2 for some b ∈ Z}.

Thanks in advance.
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