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A unit is an element in a Ring that has a multiplicative inverse. If $n$ is an Algebraic Integer which divides every Algebraic Integer in the Field, $n$ is called a unit in that Field. A given Field may contain an infinity of units. The units of $\Bbb{Z}_n$ are the elements Relatively Prime to $n$. The units in $\Bbb{Z}_n$ which are Squares are called Quadratic Residues.

See also Eisenstein Unit, Fundamental Unit, Prime Unit, Quadratic Residue

© 1996-9 Eric W. Weisstein