What is $\Bbb R^{\times}$? [unit group, ring to "times" power]

I'm doing some sheets for my Abstract Algebra class and I can't seem to remember the group defined as $\mathbb{R}^{\times}$. It's obviously some variation of $\mathbb{R}$ but I'm away from college on reading week so can't ask my tutor. If someone could clear up the confusion I'd be grateful.

Solution 1:

This is the usual notation for the unit group of the ring $R$, that is, the group of invertible elements using ring multiplication as the group operation. Note that this is usually not the same thing as $R \setminus \{0\}$, because most elements aren't invertible (if it is the same, your ring is a field, by definition). While you can talk about $R \setminus \{0\}$ under multiplication, it's usually just a monoid (or even a semigroup, if you permit rings without unity).