-
function composition, the
endomorphisms of an
abelian group form a ring (the
endomorphism ring). For example, the set of
endomorphisms of Z n {\displaystyle...
- In mathematics, the
endomorphisms of an
abelian group X form a ring. This ring is
called the
endomorphism ring of X,
denoted by End(X); the set of all...
- {\displaystyle \varphi (x^{p})=\varphi (x)^{p}.} If FR and FS are the
Frobenius endomorphisms of R and S, then this can be
rewritten as: φ ∘ F R = F S ∘ φ . {\displaystyle...
-
transformation f : V → V {\textstyle f:V\to V} is an
endomorphism of V {\textstyle V} ; the set of all such
endomorphisms End ( V ) {\textstyle \operatorname {End}...
- \operatorname {End} _{R}(M)=\operatorname {Hom} _{R}(M,M)} for the set of all
endomorphisms of a
module M. It is not only an
abelian group but is also a ring with...
-
complex multiplication theory of
abelian varieties A
having enough endomorphisms in a
certain precise sense,
roughly that the
action on the
tangent space...
- of
prime characteristic p, R → R, x → xp is a ring
endomorphism called the
Frobenius endomorphism. If R and S are rings, the zero
function from R to S...
- In
linear algebra, the
trace of a
square matrix A,
denoted tr(A), is the sum of the
elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...
-
corner ring of R. The
corner ring
arises naturally since the ring of
endomorphisms EndR(aR) ≅ aRa. The
idempotents of R have an
important connection to...
- with
identical source and target) is an
endomorphism of X. A
split endomorphism is an
idempotent endomorphism f if f
admits a
decomposition f = h ∘ g...
