Definition & Betydelse | Engelska ordet ENDOMORPHISM

Definition av ENDOMORPHISM

1. (matematik) endomorfi

Exempel på hur man kan använda ENDOMORPHISM i en mening

• Under this addition, and with multiplication being defined as function composition, the endomorphisms of an abelian group form a ring (the endomorphism ring).
• In particular, one obtains the notions of ring endomorphism, ring isomorphism, and ring automorphism.
• Addition of endomorphisms arises naturally in a pointwise manner and multiplication via endomorphism composition.
• For vector spaces, the scalar transforms are exactly the center of the endomorphism algebra, and, similarly, scalar invertible transforms are the center of the general linear group GL(V).
• Deligne's contribution was to supply the estimate of the eigenvalues of the Frobenius endomorphism, considered the geometric analogue of the Riemann hypothesis.
• A module homomorphism from a module M to itself is called an endomorphism and an isomorphism from M to itself an automorphism.
• However, this is a stricter notion, since the endomorphism ring of a countably infinite dimensional vector space is semiprimitive, but not a subdirect product of simple rings,.
• While projective covers for modules do not always exist, it was speculated that for general rings, every module would have a flat cover, that is, every module M would be the epimorphic image of a flat module F such that every map from a flat module onto M factors through F, and any endomorphism of F over M is an automorphism.
• More generally, a ring of characteristic p (p a prime) is called perfect if the Frobenius endomorphism is an automorphism.
• If M is indecomposable and has finite length, then every endomorphism of M is either an automorphism or nilpotent.
• If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism of A to itself, which is a derivation over K.
• The endomorphism ring of a semisimple module is not only semiprimitive, but also von Neumann regular.
• The possible types of endomorphism ring have been classified, as rings with involution (the Rosati involution), leading to a classification of CM-type abelian varieties.
• It follows that, over the reals, if the matrix of an endomorphism is symmetric, then it is diagonalizable.
• In the theory of superalgebras, if A is a commutative superalgebra, V is a free right A-supermodule and T is an endomorphism from V to itself, then the supertrace of T, str(T) is defined by the following trace diagram:.
• In positive characteristic it is possible for the endomorphism ring to be even larger: it can be an order in a quaternion algebra of dimension 4, in which case the elliptic curve is supersingular.
• Any endomorphism f of a dualizable object admits a trace, which is a certain endomorphism of the monoidal unit of C.
• The classic reason (due to Serre) is that if X is a supersingular elliptic curve, then its endomorphism ring is a maximal order in a quaternion algebra B over Q ramified at p and ∞.
• In mathematics, the Auslander algebra of an algebra A is the endomorphism ring of the sum of the indecomposable modules of A.
• For p-adic curves the analogue of complex conjugation is the Frobenius endomorphism, and the analogue of the quasi-Fuchsian condition is an integrality condition on the indigenous line bundle.

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