# Unit divisor

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 15-XX *Secondary:* 13A05 [MSN][ZBL]

An element $a$ of a ring (with a unit element 1) for which there exists an inverse, i.e. an element $b$ such that $ab=ba=1$. In the theory of algebraic numbers and algebraic functions such elements are also called units.

#### Comments

The phrases divisor of unity or invertible element are also used for this notion.

See Divisibility in rings for the general theory.

**How to Cite This Entry:**

Unit divisor.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Unit_divisor&oldid=35236

This article was adapted from an original article by O.A. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article