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Center (ring theory)

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In algebra, the center of a ring R is the subring consisting of the elements x such that xy = yx for all elements y in R. It is a commutative ring and is denoted as Z(R); 'Z' stands for the German word Zentrum, meaning "center".

If R is a ring, then R is an associative algebra over its center. Conversely, if R is an associative algebra over a commutative subring S, then S is a subring of the center of R, and if S happens to be the center of R, then the algebra R is called a central algebra.

Examples

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See also

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Notes

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  1. ^ "vector spaces – A linear operator commuting with all such operators is a scalar multiple of the identity". Math.stackexchange.com. Retrieved July 22, 2017.

References

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