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I saw the term "a ring with unity", and wikipedia mentions that unity refers to the identity element $1_R$ of the ring. So is a ring with unity the same as a ring with identity?

Thanks!

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    thanks for the clarifications!2011-04-20

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Unity means a multiplicative identity, in the same way that things which are nth roots of 1 in the field $\mathbb{C}$ are called roots of "unity".