Difference between revisions of "Unit divisor"
From Encyclopedia of Mathematics
(Importing text file) |
(MSC 15 13A05) |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | An element | + | {{TEX|done}}{{MSC|15|13A05}} |
| + | |||
| + | 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. | ||
| Line 5: | Line 7: | ||
====Comments==== | ====Comments==== | ||
The phrases divisor of unity or invertible element are also used for this notion. | The phrases divisor of unity or invertible element are also used for this notion. | ||
| + | |||
| + | See [[Divisibility in rings]] for the general theory. | ||
Latest revision as of 22:27, 30 November 2014
2020 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://encyclopediaofmath.org/index.php?title=Unit_divisor&oldid=15747
Unit divisor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unit_divisor&oldid=15747
This article was adapted from an original article by O.A. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article