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?
2026-05-16 03:27:33.1778902053
Ring commutative with a 1
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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 $1$).