Let R be the ring of integers in . Determine the units in R.

Let be a unit of R, then the norm of x, that is,

I can only think of +1 and -1 being units in R, anything more?

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- February 24th 2008, 01:16 PMtttcomraderFind units in ring of integers
Let R be the ring of integers in . Determine the units in R.

Let be a unit of R, then the norm of x, that is,

I can only think of +1 and -1 being units in R, anything more? - February 26th 2008, 05:46 AMJaneBennet
A unit in a ring with multipicative identity 1 is a divisor of 1; if the ring is also a normed vector space, then the norm of a unit must be 1.

So is a unit in ..

Conversely, any element of the form where is a unit in , its mutliplicative inverse being :

Hence the units of are .

By the way, there are units other than ±1: for example, .