Search results
Results From The WOW.Com Content Network
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 ...
The center of a commutative ring R is R itself. The center of a skew-field is a field. The center of the (full) matrix ring with entries in a commutative ring R consists of R-scalar multiples of the identity matrix. [1] Let F be a field extension of a field k, and R an algebra over k. Then Z(R ⊗ k F) = Z(R) ⊗ k F.
A strict definition of a triangle centre is a point whose trilinear coordinates are f(a,b,c) : f(b,c,a) : f(c,a,b) where f is a function of the lengths of the three sides of the triangle, a, b, c such that: f is homogeneous in a, b, c; i.e., f(ta,tb,tc)=t h f(a,b,c) for some real power h; thus the position of a centre is independent of scale.
The kernel of the map G → G i is the i th center [1] of G (second center, third center, etc.), denoted Z i (G). [2] Concretely, the (i+1)-st center comprises the elements that commute with all elements up to an element of the i th center. Following this definition, one can define the 0th center of a group to be the identity subgroup.
Extending the above-mentioned braiding on the center of an ordinary monoidal category, the center of a monoidal ∞-category becomes an -monoidal category. More generally, the center of a E k {\displaystyle E_{k}} -monoidal category is an algebra object in E k {\displaystyle E_{k}} -monoidal categories and therefore, by Dunn additivity , an E k ...
Rather than characterize mathematics by deductive logic, intuitionism views mathematics as primarily about the construction of ideas in the mind: [9] The only possible foundation of mathematics must be sought in this construction under the obligation carefully to watch which constructions intuition allows and which not. [12] L. E. J. Brouwer 1907
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the figure. The same definition extends to any object in n {\displaystyle n} - dimensional Euclidean space .
In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example, the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained by simple constructions.