What is a group of units in a ring?

Using units you can also define the idea of an “associate” which lets you generalize the fundamental theore The units in a ring are those elements which have an inverse under multiplication. They form a group, and this “group of units” is very important in algebraic number theory.

Who authored the group of units?

This page titled 5: The Group of Units is shared under a not declared license and was authored, remixed, and/or curated by W. Edwin Clark via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

What is a group of units of R called?

The set of units of R forms a group R× under multiplication, called the group of units or unit group of R. [b] Other notations for the unit group are R∗, U (R), and E (R) (from the German term Einheit ).