center (rings)

If $A$ is a ring, the center of $A$, sometimes denoted $\mathrm{Z}(A)$, is the set of all elements in $A$ that commute with all other elements of $A$. That is,

$$\mathrm{Z}(A)=\{a\in A\mid ax=xa\forall x\in A\}$$

Note that $0\in \mathrm{Z}(A)$ so the center is non-empty. If we assume that $A$ is a ring with a multiplicative unity $1$, then $1$ is in the center as well. The center of $A$ is also a subring of $A$.

Title	center (rings)
Canonical name	Centerrings
Date of creation	2013-03-22 12:45:29
Last modified on	2013-03-22 12:45:29
Owner	drini (3)
Last modified by	drini (3)
Numerical id	6
Author	drini (3)
Entry type	Definition
Classification	msc 16U70
Synonym	center
Related topic	GroupCentre