Universal side divisor: Difference between revisions

Revision as of 23:53, 22 January 2009

A nonzero element $x$ in an commutative unital ring $R$ is termed a universal side divisor if $x$ satisfies the following two conditions:

$x$ is not a unit.
For any $y\in R$ , either $x$ divides $y$ or there exists a unit $u\in R$ such that $x$ divides $y-u$ .

@@ Line 4: / Line 4: @@
 * <math>x</math> is not a unit.
-* For any <math>y \in R</math>, there exists a unit <math>u \in R</math> such that <math>x</math> divides <math>y - u</math>.
+* For any <math>y \in R</math>, either <math>x</math> divides <math>y</math> or there exists a unit <math>u \in R</math> such that <math>x</math> divides <math>y - u</math>.
 ==Facts==
 * [[Euclidean domain that is not a field has a universal side divisor]]