endomorphisms's Usage Examples:

In general, we can talk about endomorphisms in any category.

In the category of sets, endomorphisms are functions from a set S to itself.

In abstract algebra, the endomorphisms of an abelian group X form a ring.

negation from the endomorphisms of the group (the "additive closure" of the set of endomorphisms).

If G is abelian then the set of endomorphisms is already additively.

the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense (it roughly means that the action on the.

of endomorphisms of the free right R-module of rank n; that is, Mn(R) ≅ EndR(Rn).

Matrix multiplication corresponds to composition of endomorphisms.

at one times used to refer to complex elliptic curves whose ring of endomorphisms has rank 2, the maximum possible.

every endomorphism of the abelian group M which commutes with all R-endomorphisms of M is given by multiplication by a ring element.

f:V\rightarrow V} is an endomorphism of V {\textstyle V} ; the set of all such endomorphisms End ⁡ ( V ) {\textstyle \operatorname {End} (V)} together with addition.

ring, which is generated over the ring of Witt vectors by two special endomorphisms F and V called the Frobenius and Verschiebung operators.

The Sturmian endomorphisms form a submonoid of the monoid of endomorphisms of B∗.

Define endomorphisms φ and ψ of B∗, where B = {0,1}.

})_{\omega \in \Omega }} of endomorphisms of G.

The associate endomorphisms are called the homotheties.

considering the (formal) endomorphisms of the formal group, emulating the way in which elliptic curves with extra endomorphisms are used to give abelian.

symplectic group, identified with the group of quaternionic-linear unitary endomorphisms of a k {\displaystyle k} -dimensional quaternionic Hermitian space).

representation of G on a vector space V with a linear map from the endomorphisms of V into V 's underlying field.