Center (algebra)

The term center or centre is used in various contexts in

commute

with all other elements.

The
center of a group G consists of all those elements x in G such that xg = gx for all g in G. This is a normal subgroup
of G.

The similarly named notion for a semigroup is defined likewise and it is a subsemigroup.^[1]^[2]
The center of a ring (or an associative algebra) R is the subset of R consisting of all those elements x of R such that xr = rx for all r in R.^[3] The center is a commutative subring of R.
The
center of a Lie algebra L 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.

References

ISBN 978-3-11-015248-7
.

ISBN 978-0-8218-8641-0
.

ISBN 0-471-51001-7
. The center of a ring R is defined to be {c ∈ R: cr = rc for every r ∈ R}., Exercise 22.22

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Retrieved from "https://en.wikipedia.org/w/index.php?title=Center_(algebra)&oldid=977333858"

[KilpKilʹp2000-1] ISBN 978-3-11-015248-7
.

[Ljapin1968-2] ISBN 978-0-8218-8641-0
.

[3] ISBN 0-471-51001-7
. The center of a ring R is defined to be {c ∈ R: cr = rc for every r ∈ R}., Exercise 22.22

[1]

[2]

[3]

See also

References