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# Algebra

## Definition of the noun algebra

What does algebra mean as a name of something?

noun - plural: algebras

1. the mathematics of generalized arithmetical operations
• examples: Many pupils are poor at algebra. | Algebra is a branch of mathematics. | Algebra is my favorite subject. | In algebra a monomorphism is an injective homomorphism. | It was innovation in Muslim communities that developed the order of algebra; our magnetic compass and tools of navigation; our mastery of pens and printing; our understanding of how disease spreads and how it can be healed. | I tried explaining the algebra homework to him, but it just went in one ear and out the other. | An affine algebraic group over a field k is a representable covariant functor from the category of commutative algebras over k to the category of groups such that the representing algebra is finitely generated. | People tend to consider translation like algebra, with both sides of the equation being identical, when in fact it's more like a cover version of a song, where the tune is the same, but the arrangement is unique. | In algebra, we often replace numbers with letters.
• domain: math / mathematics / maths
• lexical domain: Cognitive Processes - nouns denoting cognitive processes and contents
• more generic term: pure mathematics = the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness
• more specific terms:
• linear algebra = the part of algebra that deals with the theory of linear equations and linear transformation
• vector algebra = the part of algebra that deals with the theory of vectors and vector spaces
• matrix algebra = the part of algebra that deals with the theory of matrices

### Alternative definition of the noun algebra

noun

1. [uncountable, mathematics] A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols
2. [uncountable, mathematics] The study of algebraic structures
3. [countable, mathematics] A universal algebra
4. [countable, algebra] An algebraic structure consisting of a module of a commutative ring along with an additional binary operation that is bilinear
5. [countable, set theory, analysis] 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)
6. [countable, mathematics] One of several other types of mathematical structure

## Person

Who is Algebra?

Algebra is an American contemporary R&B singer.

• also known as Algebra Felicia Blesset
• born in (40 years ago) in Atlanta
• profession: Singer-songwriter
• genres: Contemporary R&B, Neo soul
• albums: "Procreation", "Purpose", "Polymorph", "Recovery", "Feed the Ego"

## Writings

"Algebra" is a book by Michael Artin.

• subject: Matrix

## Music

1. "Algebra" is a musical album of ACYL.
2. "Algebra" is a musical album of Piotr Kaliński.
• released on
3. "Algebra" is a musical EP of Airship.
• released on (5 years ago)

## Miscellanea

1. Algebra: In mathematics, specifically in ring theory, an algebra over a commutative ring is a generalization of the concept of an algebra over a field, where the base field K is replaced by a commutative ring R.
• also known as 代數
2. Algebra a.k.a. *-algebra: In mathematics, and more specifically in abstract algebra, a *-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.
3. Algebra a.k.a. †-algebra: A †-algebra is the name occasionally used in physics for a finite-dimensional C*-algebra. The dagger, †, is used in the name because physicists typically use the symbol to denote a hermitian adjoint, and are often not worried about the subtleties associated with an infinite number of dimensions. †-algebras feature prominently in quantum mechanics, and especially quantum information science.

## Printed encyclopedias and other books with definitions for Algebra

Click on a title to look inside that book (if available):

### Algebraic Geometry (1998)

by Daniel Bump

More precisely, an affine algebra is a finitely generated fc-algebra which is an integral domain.

### Algebraic Theories (2012)

by Ernest Manes

A Boolean algebra is a commutative ring with unit (X, +, 0, jux, 1) (where “jux” indicates that we will write multiplication by juxtaposition) in which multiplication is idempotent: xx = x. See [Halmos '63]. The standard example is the set of all ...

### Teaching and Learning Algebra (2005)

by Doug French

Algebra is a vital part of mathematics and is increasingly accepted as an important element of the school mathematics curriculum for most, if not all, students. Algebra is a powerful tool for solving problems in the 'real' world, but besides its ...

### Computer Analysis of Images and Patterns (1997)

7th International Conference, CAIP '97, Kiel, Germany, September 10-12, 1997. Proceedings. by Gerald Sommer, Kostas Daniilidis, Josef Pauli

Geometric algebra is a coordinate- free approach to geometry based on the algebras of Grassmann [5] and Clifford [3] - the approach we adopt here...

### Max-Plus Methods for Nonlinear Control and Estimation (2006)

by William M. McEneaney

The max-plus algebra is a commutative semifield which has come under intense study in the last decade.

### Measure Theory (2008)

by D. H. Fremlin

A Maharam algebra is a Dedekind σ-complete Boolean algebra with a strictly positive Maharam submeasure.

If μ is any Maharam submeasure on a Dedekind σ-complete Boolean algebra A, its Maharam algebra is the quotient A/{ a : μa ...

### Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (2003)

by I. Grattan-Guinness

solid grounding in practical mathematics - arithmetic and geometry and sometimes also algebra. Most of these students intended to pursue a career as a merchant; others were would-be cartographers, artists, architects. The heads of these ...

### Encyclopedia of Parallel Computing (2011)

Area-Universal Networks Array Languages Array Languages, Compiler Techniques for Asynchronous Iterations Asynchronous Iterative Algorithms Asynchronous Iterative Computations ATLAS (Automatically Tuned Linear Algebra Software) ...

### Concise Encyclopedia of Computer Science (2004)

by Edwin D. Reilly

BOOLEAN ALGEBRA For articles on related subjects, see + Arithmetic, Computer + Discrete Mathematics + Logic Design + Logic Programming The concept of a Boolean algebra was first proposed by the English mathematician George Boole ...

## Online dictionaries and encyclopedias with entries for Algebra

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## Video language resources about Algebra

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View more videos about Linear algebra, Boolean algebra, and Abstract algebra.

## Sign language

Algebra: Evaluating Expression (American Sign Language)

Math tutoring in ASL.

We may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra. (William Kingdon Clifford)

## Scrabble value of A1L1G2E1B3R1A1

The value of this 7-letter word is 10 points. It is included in the first and second editions of the Official Scrabble Players Dictionary.

## Anagrams of ALGEBRA

What do you get if you rearrange the letters?

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