Let R be a commutative ring with unity and r ∈ R. Prove that if ⟨r⟩ = R, then r is a unit. Consider the ring (Z,⋆,⊙) - where a ⋆ b = a + b − 1 and a ⊙ b = a + b − ab. What is ⟨2⟩?

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A: Let R be a ring with unity 1R and let S be a subring of R containing 1R. If r∈R is a unit of R and…

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Q: if A, B, C are ideals of a ring R such that BCA, prove that An (B + C) = B+ (AnC) = (A B) + (AnC).

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Q: If A, B, C are ideals of a ring R such that BCA, prove that An (B + C) = B+ (AnC) = (An B) + (AnC).

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