This article is about a branch of mathematics. For the Swedish band, see Abstrakt Algebra.
"Modern algebra" redirects here. For van der Waerden's book, see Moderne Algebra.
The permutations of the Rubik's Cube form a group, a fundamental concept within abstract algebra.
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures.[1] Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra was coined in the early 20th century to distinguish it from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. The abstract perspective on algebra has become so fundamental to advanced mathematics that it is simply called "algebra", while the term "abstract algebra" is seldom used except in pedagogy.
Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory gives a unified framework to study properties and constructions that are similar for various structures.
Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the variety of groups.
^Finston, David R.; Morandi, Patrick J. (29 August 2014). Abstract Algebra: Structure and Application. Springer. p. 58. ISBN 978-3-319-04498-9. Much of our study of abstract algebra involves an analysis of structures and their operations
mathematics, more specifically algebra, abstractalgebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings...
discover the values that solve all equations at the same time. Abstractalgebra studies algebraic structures, which consist of a set of mathematical objects...
Appendix:Glossary of abstractalgebra in Wiktionary, the free dictionary. Abstractalgebra is the subject area of mathematics that studies algebraic structures...
Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...
was a German mathematician who made many important contributions to abstractalgebra. She proved Noether's first and second theorems, which are fundamental...
In abstractalgebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstractalgebra: other well-known...
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 mathematical logic, abstractalgebraic logic is the study of the algebraization of deductive systems arising as an abstraction of the well-known Lindenbaum–Tarski...
the CLU language. Algebraic specification was an important subject of research in CS around 1980 and almost a synonym for abstract data types at that...
addition to single and multivariable real analysis as well as abstract linear algebra. In 1970, for example, students studied the differential geometry...
(called vectors). Abstractalgebra is the name that is commonly given to the study of algebraic structures. The general theory of algebraic structures has...
studies abstractalgebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic...
when many ideas and methods of previous centuries were generalized as abstractalgebra. The development of computers led to increased research in efficient...
In abstractalgebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A =...
Algebraic geometry is a branch of mathematics which uses abstractalgebraic techniques, mainly from commutative algebra, to solve geometrical problems...
In mathematics: In abstractalgebra and mathematical logic a derivative algebra is an algebraic structure that provides an abstraction of the derivative...
Algebraic topology is a branch of mathematics that uses tools from abstractalgebra to study topological spaces. The basic goal is to find algebraic invariants...
In mathematics, specifically abstractalgebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship...
In abstractalgebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital)...
In ring theory, a branch of abstractalgebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite...
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...
In abstractalgebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior...
treatment of abstract homological algebra, unifying previously disparate presentations of homology and cohomology for associative algebras, Lie algebras, and...
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