characteristic endomorphism
1Characteristic subgroup — In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group.[1][2] Because conjugation is an automorphism, every… …
2Frobenius endomorphism — In commutative algebra and field theory, which are branches of mathematics, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of rings with prime characteristic p , a class importantly including fields. The… …
3Fully characteristic subgroup — In mathematics, a subgroup of a group is fully characteristic (or fully invariant) if it is invariant under every endomorphism of the group. That is, any endomorphism of the group takes elements of the subgroup to elements of the subgroup.Every… …
4Trace Zero Cryptography — In the year 1998 Gerhard Frey firstly purposed using trace zero varieties for cryptographic purpose. These varieties are subgroups of the divisor class group on a low genus hyperelliptic curve defined over a finite field. These groups can be used …
5Cayley–Hamilton theorem — In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Hamilton) states that every square matrix over the real or complex field satisfies its own characteristic equation.More precisely; if A is… …
6Minimal polynomial (linear algebra) — For the minimal polynomial of an algebraic element of a field, see Minimal polynomial (field theory). In linear algebra, the minimal polynomial μA of an n by n matrix A over a field F is the monic polynomial P over F of least degree such that… …
7Algebraically closed field — In mathematics, a field F is said to be algebraically closed if every polynomial in one variable of degree at least 1, with coefficients in F , has a root in F . ExamplesAs an example, the field of real numbers is not algebraically closed,… …
8Modular representation theory — is a branch of mathematics, and that part of representation theory that studies linear representations of finite group G over a field K of positive characteristic. As well as having applications to group theory, modular representations arise… …
9Supersingular elliptic curve — In algebraic geometry, a branch of mathematics, supersingular elliptic curves form a certain class of elliptic curves over a field of characteristic p > 0. Elliptic curves over such fields which are not supersingular are called… …
10Perfect field — In algebra, a field k is said to be perfect if any one of the following equivalent conditions holds: Every irreducible polynomial over k has distinct roots. Every polynomial over k is separable. Every finite extension of k is separable. (This… …
