Universal side divisor: Difference between revisions

Revision as of 23:35, 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 $y \in R$ , there exists a unit $u \in R$ such that $x$ divides $y - u$ .

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 ==Definition==
-A nonzero element <math>x</math> in an [[integral domain]] <math>R</math> is termed a '''universal side divisor''' if <math>x</math> satisfies the following two conditions:
+A nonzero element <math>x</math> in an [[commutative unital ring]] <math>R</math> is termed a '''universal side divisor''' if <math>x</math> satisfies the following two conditions:
 * <math>x</math> is not a unit.