Wondering how to use Algebra in a sentence? Below are 10+ example sentences from authentic English texts. Including the meaning .
Algebra in a sentence
Related words
Algebra meaning
- Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations.
- Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms).
- Any of several objects of study in Algebra
Synonyms of Algebra
Using Algebra
- The main meaning on this page is: Elementary algebra: A system for representing and manipulating unknown quantities (variables) in equations. | Abstract algebra: A broad field of study in modern mathematics (often mentioned alongside analysis) loosely characterized by its concern for abstraction and symmetry, dealing with the behavior, classification, and application of a large class of objects (called algebraic structures) and the maps between them (called, most generally, morphisms). | Any of several objects of study in Algebra
- Useful related words include: pure mathematics.
- In the example corpus, algebra often appears in combinations such as: lie algebra, algebra is, algebra and.
Context around Algebra
- Average sentence length in these examples: 26.7 words
- Position in the sentence: 11 start, 9 middle, 0 end
- Sentence types: 19 statements, 1 questions, 0 exclamations
Corpus analysis for Algebra
- In this selection, "algebra" usually appears near the start of the sentence. The average example has 26.7 words, and this corpus slice is mostly made up of statements.
- Around the word, lie, boolean, division, almost, see and abstract stand out and add context to how "algebra" is used.
- Recognizable usage signals include a lie algebra over the, simple k algebra is a and lie algebra. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "algebra" sits close to words such as activate, bonding and cherished, which helps place it inside the broader word index.
Example types with algebra
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Algebra *Any ring A can be considered as a Z-algebra. (11 words)
Also, we mostly fix the base field; thus, an algebra refers to a k-algebra. (15 words)
Ado's theorem says every finite-dimensional Lie algebra is isomorphic to a matrix Lie algebra. (16 words)
A locally compact group is said to be of type I if and only if its group C*-algebra is type I. However, if a C*-algebra has non-type I representations, then by results of James Glimm it also has representations of type II and type III. (48 words)
Type for C*-algebras A C*-algebra A is of type I if and only if for all non-degenerate representations π of A the von Neumann algebra π(A)′′ (that is, the bicommutant of π(A)) is a type I von Neumann algebra. (44 words)
The definition of finite groups of Lie type due to Chevalley involves restricting from a Lie algebra over the complex numbers to a Lie algebra over the integers, and the reducing modulo p to get a Lie algebra over a finite field. (42 words)
Calling (1), (2), and (4) a Robbins algebra, the question then becomes: Is every Robbins algebra a Boolean algebra? (19 words)
Example sentences (20)
Representation theory * The universal enveloping algebra of a Lie algebra is an associative algebra that can be used to study the given Lie algebra.
A Boolean algebra with only one element is called a trivial Boolean algebra or a degenerate Boolean algebra.
A central simple algebra over K is a matrix algebra over a (finite dimensional) division algebra with center K. For example, the central simple algebras over the reals are matrix algebras over either the reals or the quaternions.
A Lie algebra is solvable if and only if Classification The Levi decomposition expresses an arbitrary Lie algebra as a semidirect sum of its solvable radical and a semisimple Lie algebra, almost in a canonical way.
Calling (1), (2), and (4) a Robbins algebra, the question then becomes: Is every Robbins algebra a Boolean algebra?
For every finite-dimensional matrix Lie algebra, there is a linear group (matrix Lie group) with this algebra as its Lie algebra.
Since the center of a simple k-algebra is a field, any simple k-algebra is a central simple algebra over its center.
The definition of finite groups of Lie type due to Chevalley involves restricting from a Lie algebra over the complex numbers to a Lie algebra over the integers, and the reducing modulo p to get a Lie algebra over a finite field.
The most familiar Clifford algebra, or orthogonal Clifford algebra, is also referred to as Riemannian Clifford algebra. see for ex.
Type for C*-algebras A C*-algebra A is of type I if and only if for all non-degenerate representations π of A the von Neumann algebra π(A)′′ (that is, the bicommutant of π(A)) is a type I von Neumann algebra.
Abstract algebra Abstract algebra employs several types of sequences, including sequences of mathematical objects such as groups or rings.
A C*-algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: * A is a topologically closed set in the norm topology of operators.
Ado's theorem says every finite-dimensional Lie algebra is isomorphic to a matrix Lie algebra.
Algebra *Any ring A can be considered as a Z-algebra.
Al-Karaji (born 953) completely freed algebra from geometrical operations and replaced them with the arithmetical type of operations which are at the core of algebra today.
A locally compact group is said to be of type I if and only if its group C*-algebra is type I. However, if a C*-algebra has non-type I representations, then by results of James Glimm it also has representations of type II and type III.
Also, we mostly fix the base field; thus, an algebra refers to a k-algebra.
At the time George Boole 's algebra of logic made a strong counterpoint to ordinary number algebra, so the term "universal" served to calm strained sensibilities.
By the Artin–Wedderburn theorem (specifically, Wedderburn's part), CSAs are all matrix algebras over a division algebra, and thus the quaternions are the only non-trivial division algebra over the reals.
Diophantus' work created a foundation for work on algebra and in fact much of advanced mathematics is based on algebra.
Phrases with algebra
These phrases have their own page with example sentences containing the full combination:
Common combinations with algebra
These word pairs occur most frequently in English texts:
- lie algebra 41×
- algebra is 33×
- algebra and 16×
- algebra of 13×
- algebra over 13×
- boolean algebra 12×
- of algebra 12×
- an algebra 11×
- geometric algebra 11×
- abstract algebra 10×