Thread: Units

What are the units of Z? In other words find Z^x.

Here is some background:

Every element in a ring has an additive inverse, but only some elements
have multiplicative inverses. Any element with a multiplicative inverse is
called a

unit. Recall that we assume all rings have a multiplicative identity.

Let R be a ring with multiplicative identity 1. If a, b eR are
such that ab = ba = 1 then we say that a and b are multiplicative inverses.

An element a e R is called a unit if it has an inverse. The set of units is
written R:

R^x = {u e R | u is a unit}

Hello jzellt

Originally Posted by jzellt

What are the units of Z? In other words find Z^x.

Here is some background:

Every element in a ring has an additive inverse, but only some elements
have multiplicative inverses. Any element with a multiplicative inverse is
called a

unit. Recall that we assume all rings have a multiplicative identity.

Let R be a ring with multiplicative identity 1. If a, b eR are
such that ab = ba = 1 then we say that a and b are multiplicative inverses.

An element a e R is called a unit if it has an inverse. The set of units is
written R:

R^x = {u e R | u is a unit}

In , all non-zero elements, , have a multiplicative inverse, . But in will not be an integer unless ?

Grandad