\mathbb {Z} } , so the characteristic of C {\displaystyle \mathbb {C} } is 0. A Z / n Z {\displaystyle \mathbb {Z} /n\mathbb {Z} } -algebra is equivalently a...

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure...

and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics...

In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear...

of k is separable. Every algebraic extension of k is separable. Either k has characteristic 0, or, when k has characteristic p > 0, every element of k...

current–voltage characteristic, the current in a circuit as a function of the applied voltage Receiver operating characteristic Characteristic (algebra) of a ring...

otherwise stated, a Lie algebra is a finite-dimensional Lie algebra over a field of characteristic 0. For such a Lie algebra g {\displaystyle {\mathfrak...

mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is a commutative algebra over K that contains V, and...

Lie algebra g {\displaystyle {\mathfrak {g}}} over a field of characteristic 0 {\displaystyle 0} . In a finite-dimensional semisimple Lie algebra over...

mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: x y = y x {\displaystyle...

specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological...

A_{n}} with underlying field F {\displaystyle F} characteristic zero, unless otherwise stated. The Weyl algebra is an example of a simple ring that is not a...

Appendix:Glossary of abstract algebra in Wiktionary, the free dictionary. Abstract algebra is the subject area of mathematics that studies algebraic structures, such...

Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

Universal algebra is still more abstract in that it is not interested in specific algebraic structures but investigates the characteristics of algebraic structures...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital associative) algebra and a (counital coassociative)...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative...

mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is mapped to itself by...

In mathematics, the Iwasawa algebra Λ(G) of a profinite group G is a variation of the group ring of G with p-adic coefficients that take the topology...

vectors. The characteristic function of a cooperative game in game theory. The characteristic polynomial in linear algebra. The characteristic state function...

unifying geometric concepts in algebraic topology, differential geometry, and algebraic geometry. The notion of characteristic class arose in 1935 in the...

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...

all finite fields of a fixed characteristic p (p prime) is an algebraically closed field, which is, in fact, the algebraic closure of the field F p {\displaystyle...

mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...