algebraˈæl dʒə brə

**algebra** (n)

- plural
- algebras

### English Definitions:

#### algebra (noun)

the mathematics of generalized arithmetical operations

#### algebra (Noun)

A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols

#### algebra (Noun)

The study of algebraic structures

#### algebra (Noun)

A universal algebra

#### algebra (Noun)

An algebraic structure consisting of a module of a commutative ring along with an additional binary operation that is bilinear

#### algebra (Noun)

A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences)

#### algebra (Noun)

One of several other types of mathematical structure

#### Algebra

Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers. ⁕As a single word without article, "algebra" names a broad part of mathematics. ⁕As a single word with article or in plural, "algebra" denote a specific mathematical structure. See algebra and algebra over a field. ⁕With a qualifier, there is the same distinction: ⁕Without article, it means a part of algebra, like linear algebra, elementary algebra, or abstract algebra. ⁕With an article, it means an instance of some abstract structure, like a Lie algebra or an associative algebra. ⁕Frequently both meanings exist for the same qualifier, like in the sentence: Commutative algebra is the study of commutative rings, that all are commutative algebras over the integers. ⁕Sometimes "algebra" is also used to denote the operations and methods related to algebra in the study of a structure that does not belong to algebra. For example algebra of infinite series may denotes the methods for computing with series without using the notions of infinite summation, limits and convergence.

#### Algebra

Algebra (from Arabic الجبر (al-jabr) 'reunion of broken parts, bonesetting') is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.Elementary algebra deals with the manipulation of variables as if they were numbers (see the image), and is therefore essential in all applications of mathematics. Abstract algebra is the name given in education to the study of algebraic structures such as groups, rings, and fields. Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra and some not, such as Galois theory. The word algebra is not only used for naming an area of mathematics and some subareas; it is also used for naming some sorts of algebraic structures, such as an algebra over a field, commonly called an algebra. Sometimes, the same phrase is used for a subarea and its main algebraic structures; for example, Boolean algebra and a Boolean algebra. A mathematician specialized in algebra is called an algebraist.

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"algebra." *Kamus.net.* STANDS4 LLC, 2024. Web. 23 May 2024. <https://www.kamus.net/english/algebra>.

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