Definition, Betydelse, Synonymer & Anagram | Engelska ordet ALGEBRA

Definition av ALGEBRA

1. algebra

Exempel på hur man kan använda ALGEBRA i en mening

• By contrast, the fundamental theorem of algebra states that the field of complex numbers is algebraically closed.
• He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis), pioneered the field complex analysis, and the study of permutation groups in abstract algebra.
• Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.
• His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics.
• In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center of A.
• In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed.
• In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative.
• A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values.
• Schelter is credited with the development of the GNU Common Lisp (GCL) implementation of Common Lisp and the GPL'd version of the computer algebra system Macsyma called Maxima.
• Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case.
• For example, one cannot define all the trigonometric functions in a Banach algebra without identity.
• In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
• Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
• A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties:.
• In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is mapped to itself by every automorphism of the parent group.
• Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized mathematics by allowing the expression of problems of geometry in terms of algebra and calculus.
• Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory).
• It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra.
• In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.
• In algebra, a division ring, also called a skew field (or, occasionally, a sfield), is a nontrivial ring in which division by nonzero elements is defined.

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