GF(2)(also denoted , Z/2Z or ) is the finite field of two elements (GF is the initialism of Galois field, another name for finite fields). Notations Z_2 and may be encountered although they can be confused with the notation of 2-adic integers. GF(2) is the field with the smallest possible number of elements, and is unique if the additive identity and the multiplicative identity are denoted respectively 0 and 1, as usual. The elements of GF(2) may be identified with the two possible values of a bit and to the boolean values true and false.
Cyclic permutationIn mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation has k elements, it may be called a k-cycle. Some authors widen this definition to include permutations with fixed points in addition to at most one non-trivial cycle. In cycle notation, cyclic permutations are denoted by the list of their elements enclosed with parentheses, in the order to which they are permuted.
Dagger categoryIn , a branch of mathematics, a dagger category (also called involutive category or category with involution) is a equipped with a certain structure called dagger or involution. The name dagger category was coined by Peter Selinger. A dagger category is a category equipped with an involutive contravariant endofunctor which is the identity on . In detail, this means that: for all morphisms , there exist its adjoint for all morphisms , for all objects , for all and , Note that in the previous definition, the term "adjoint" is used in a way analogous to (and inspired by) the linear-algebraic sense, not in the category-theoretic sense.
*-algebraIn mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints.
