commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic...

In mathematics, an endomorphism is a morphism from a mathematical object to itself. An endomorphism that is also an isomorphism is an automorphism. For...

endomorphism Frobenius inner product Frobenius norm Frobenius method Frobenius group Frobenius theorem (differential topology) Georg Ludwig Frobenius...

In mathematics, the Frobenius endomorphism is defined in any commutative ring R that has characteristic p, where p is a prime number. Namely, the mapping...

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...

\sigma (x):=x^{p}+p\delta (x)} defines a ring endomorphism which is a lift of the Frobenius endomorphism. When the ring R is p-torsion free the correspondence...

under the Frobenius endomorphism F*. Brion & Kumar (2005) give a detailed discussion of Frobenius splittings. A fundamental property of Frobenius-split projective...

has characteristic 0, or, when k has characteristic p > 0, the Frobenius endomorphism x ↦ xp is an automorphism of k. The separable closure of k is algebraically...

If R is an integral domain of prime characteristic p, then the Frobenius endomorphism x ↦ xp is injective. The Wikibook Abstract algebra has a page on...

of the trace of the Frobenius endomorphism on its cohomology groups. There are several generalizations: the Frobenius endomorphism can be replaced by a...

F[X] (where F is assumed to have prime characteristic p). If the Frobenius endomorphism x ↦ x p {\displaystyle x\mapsto x^{p}} of F is not surjective, there...

an endomorphism whose square is the endomorphism αφ associated to the Frobenius endomorphism φ of the field F. Roughly speaking, this endomorphism απ...

≠ p {\displaystyle l\neq p} , we make use of the theory of the Frobenius endomorphism ϕ {\displaystyle \phi } and division polynomials. Note that considering...

module), and is necessarily a group endomorphism of the abelian group (M, +). The set of all group endomorphisms of M is denoted EndZ(M) and forms a ring...

Frobenius endomorphism (also known as Frobenius morphism, Frobenius map) Frobenius determinant theorem Frobenius formula Frobenius group Frobenius complement...

duality theories. Frobenius algebras began to be studied in the 1930s by Richard Brauer and Cecil Nesbitt and were named after Georg Frobenius. Tadashi Nakayama...

lemma implies that the endomorphism ring commuting with the group action is a real associative division algebra and by the Frobenius theorem can only be...

all R-linear maps forms a ring, also called the endomorphism ring and denoted by EndR(V). The endomorphism ring of an elliptic curve. It is a commutative...

characteristic n is a (Z/nZ)-algebra in the same way. Given an R-module M, the endomorphism ring of M, denoted EndR(M) is an R-algebra by defining (r·φ)(x) = r·φ(x)...

can consider the associative algebra EndK(A) of K-linear vector space endomorphism of A. We can associate to the algebra structure on A two subalgebras...

that given an a ∈ F p {\displaystyle a\in \mathbb {F} _{p}} the Frobenius endomorphism y ↦ y p {\displaystyle y\mapsto y^{p}} gives a nonzero polynomial...

direct product of an empty collection of rings is the zero ring. The endomorphism ring of the trivial group is the zero ring. The ring of continuous real-valued...

{\mathcal {O}}(X):x^{p}=0\}} so it is given by the kernel of the Frobenius endomorphism. Over characteristic 0 there is a nice classification of unipotent...

is induced by a nondiscrete valuation of rank 1, such that the Frobenius endomorphism Φ is surjective on K°/p where K° denotes the ring of power-bounded...

of algebras Ring homomorphisms • Kernel • Inner automorphism • Frobenius endomorphism Algebraic structures • Module • Associative algebra • Graded ring...

{\displaystyle k} . The Frobenius endomorphism of X ¯ {\displaystyle {\bar {X}}} (often the geometric Frobenius, or just the Frobenius), denoted by F q {\displaystyle...

then B = Ks is a regular (E, G)-ring. On Ks there is an injective Frobenius endomorphism σ : Ks → Ks sending x to xp. Given a representation G → GL(V) for...

analogous to the Wrońskian with differentiation replaced by the Frobenius endomorphism over a finite field. Alternant matrix Vandermonde matrix Peano published...

of algebras Ring homomorphisms • Kernel • Inner automorphism • Frobenius endomorphism Algebraic structures • Module • Associative algebra • Graded ring...

the associativity of the multiplication on A {\displaystyle A} .) The endomorphism ring of an F {\displaystyle F} -vector space V {\displaystyle V} with...