Unit (Ring)

Definition : Let R be a ring. u \in R is a unit if there exist v \in R such that u*v = 1_R where 1_R is the multiplicative identity.

Let R be a Ring. An element u \in R is a unit if there exists inverse element v \in R so that u*v = 1_R; 1_R is the multiplicative identity of R. For example in the integers only 1 and -1 are units since these are the only numbers that can create a product of 1. If a Ring as a unit it will not have zero divisors.

See Also : Ring, Zero Divisor

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