I have seen in a book Commutative Algebra by Reid mention of a "ring commutative with a 1". Does tha

babajijwerz

babajijwerz

Answered question

2022-05-18

I have seen in a book Commutative Algebra by Reid mention of a "ring commutative with a 1". Does that mean that addition and multiplication are commutative and that the multiplicative identity is 1 or it means that it is in some way commutative with respect to 1? Can anyone explain?

Answer & Explanation

Tyree Duke

Tyree Duke

Beginner2022-05-19Added 10 answers

In a ring, addition is always commutative, and therefore when we talk about commutative rings, what that means is that multiplication is commutative. If we add that the ring has a 1, what that means is that the ring has an identity element with respect to multiplication (denoted by 1).

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