1. ## 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}

2. ## Units

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 $\mathbb{R}$, all non-zero elements, $x$, have a multiplicative inverse, $\frac{1}{x}$. But in $\mathbb{Z}, \frac{1}{n}$ will not be an integer unless $n = ...$ ?