The term center is used in various contexts in abstract algebra to denote the set of all those elements that commute with all other elements. More specifically:
The center of a ringR is the subset of R consisting of all those elements x of R such that xr = rx for all r in R. The center is a commutativesubring of R, so R is an algebra over its center.
The center of an algebraA consists of all those elements x of A such that xa = ax for all a in A. See also: central simple algebra.
The center of a Lie algebraL consists of all those elements x in L such that [x,a] = 0 for all a in L. This is an ideal of the Lie algebra L.
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Centre is a low-lying region of France in the center of the country.
In chess, the center refers to either the central four squares (d4,e4,d5,e5) or the central 16 squares (c3-c6,d3-d6,e3-e6,f3-f6), which are strategically important in all phases of the game.
A center can also be a building or group of buildings dedicated to a particular purpose, such as: The shopping center, the dance center, the arts center, the community center, the information center, the garden center.
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