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...

\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...

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...

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...

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...

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

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...

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

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...

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

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

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...

demonstrates that exponentiation by p produces an endomorphism, known as the Frobenius endomorphism of the ring. The demand that the characteristic p...

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

quasi-Fuchsian. For p-adic curves the analogue of complex conjugation is the Frobenius endomorphism, and the analogue of the quasi-Fuchsian condition is an integrality...

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...

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...

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...

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...

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)...

mathematics, more specifically in abstract algebra, the Frobenius theorem, proved by Ferdinand Georg Frobenius in 1877, characterizes the finite-dimensional associative...

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

generally used before starting a proof of primality. Fermat quotient Frobenius endomorphism p-derivation Fractions with prime denominators: numbers with behavior...

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

mathematics. More generally, endomorphism rings of abelian groups are rarely commutative, the simplest example being the endomorphism ring of the Klein four-group...

algebra, an involution is important to the Kazhdan–Lusztig polynomial. The endomorphism ring of an elliptic curve becomes a *-algebra over the integers, where...