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How do you use Algebras in a sentence? See 10+ example sentences showing how this word appears in different contexts, plus the exact meaning.

Less frequent word

Algebras in a sentence

Related words

Algebras | Algebra

Algebras meaning

plural of algebra

Using Algebras

  • The main meaning on this page is: plural of algebra
  • In the example corpus, algebras often appears in combinations such as: lie algebras, algebras are, boolean algebras.

Context around Algebras

  • Average sentence length in these examples: 24.6 words
  • Position in the sentence: 9 start, 11 middle, 0 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

lie 6× associative 4× boolean 3× heyting 3× banach 3× clifford 2× cev 2× simple 1× matrix 1× sometimes 1×

Often after:

theorem 1× main 1× locales 1× let 1× allows 1×

Sentence patterns with Algebras

These short patterns come directly from the example sentences and show how the word is often embedded:

2 graded algebras also known 1× algebras with nonalgebraic 1× and associative algebras 1× and boolean algebras are endowed 1× and lie algebras allows one 1× are matrix algebras over either 1× article associative algebras are assumed 1× be division algebras 1×

Sentence openings and endings

Common sentence openings:

a central simple 1× a fundamental example 1× algebras with nonalgebraic 1× being lattices heyting 1× cayley dickson construction 1× clifford algebras are 1×

Common sentence endings:

algebras for clarification 1× an interval algebra 1× and associative algebras 1× any lie group 1× as the reals 1× be division algebras 1×

Words around Algebras

Just before it in the word index:

algebraist 2 algebraically 21 algebraic 280 algebra 465 algarve 37 algarotti 8

Just after it in the word index:

algeciras 16 algemeen 2 algemeiner 2 algemene 2 algeo 4 alger 42

Similar in corpus frequency:

acadia 145 adesina 145 adityanath 145 ae 145 aes 145 aguero 145

Corpus analysis for Algebras

  • In this selection, "algebras" usually appears in the middle of the sentence. The average example has 24.6 words, and this corpus slice is mostly made up of statements.
  • Around the word, lie, associative, boolean, theorem, main and locales stand out and add context to how "algebras" is used.
  • Recognizable usage signals include 2 graded algebras also known, algebras with nonalgebraic and lie algebras. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "algebras" sits close to words such as acadia, adesina and adityanath, which helps place it inside the broader word index.

Example types with algebras

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Clifford algebras are Z 2 - graded algebras (also known as superalgebras ). (11 words)

Being lattices, Heyting algebras and Boolean algebras are endowed with these monoid structures. (13 words)

More specific complete lattices are complete Boolean algebras and complete Heyting algebras (locales). (13 words)

Longer example sentences

If a Banach algebra has unit 1, then 1 cannot be a commutator ; i.e., for any x, y ∈ A. The various algebras of functions given in the examples above have very different properties from standard examples of algebras such as the reals. (43 words)

It can enable the use of methods invented for some particular classes of algebras to other classes of algebras, by recasting the methods in terms of universal algebra (if possible), and then interpreting these as applied to other classes. (39 words)

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. (38 words)

Example sentences (20)

There exists some structure theory for such algebras that generalizes the analogous results for Lie algebras and associative algebras.

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 fundamental example is the use of Boolean algebras to represent truth values in classical propositional logic, and the use of Heyting algebras to represent truth values in intuitionistic propositional logic.

Algebras with nonalgebraic structure Sometimes algebras are equipped with a nonalgebraic structure in addition to their algebraic operations.

Being lattices, Heyting algebras and Boolean algebras are endowed with these monoid structures.

Cayley–Dickson construction details All of the Clifford algebras Cℓ p,q (R) apart from the real numbers, complex numbers and the quaternions contain non-real elements that square to +1; and so cannot be division algebras.

Clifford algebras are Z 2 - graded algebras (also known as superalgebras ).

Concrete C*-algebras of compact operators admit a characterization similar to Wedderburn's theorem for finite dimensional C*-algebras: Theorem.

Advertentie

If a Banach algebra has unit 1, then 1 cannot be a commutator ; i.e., for any x, y ∈ A. The various algebras of functions given in the examples above have very different properties from standard examples of algebras such as the reals.

Interval algebras are useful in the study of Lindenbaum-Tarski algebras ; every countable Boolean algebra is isomorphic to an interval algebra.

In this article associative algebras are assumed to have a multiplicative unit, denoted 1; they are sometimes called unital associative algebras for clarification.

It can enable the use of methods invented for some particular classes of algebras to other classes of algebras, by recasting the methods in terms of universal algebra (if possible), and then interpreting these as applied to other classes.

It is however not an equivalence of categories : different Lie groups may have isomorphic Lie algebras (for example SO(3) and SU(2) ), and there are (infinite dimensional) Lie algebras that are not associated to any Lie group.

Mal'cev algebras main In the case of Mal'cev algebras, this construction can be simplified.

More specific complete lattices are complete Boolean algebras and complete Heyting algebras (locales).

Nonetheless, much of the terminology that was developed in the theory of associative rings or associative algebras is commonly applied to Lie algebras.

Tensor algebras Let C be the category of vector spaces K-Vect over a field K and let D be the category of algebras K-Alg over K (assumed to be unital and associative ).

The Stone–Weierstrass theorem mentioned above, for example, relies on Banach algebras which are both Banach spaces and algebras.

The theory of real Banach algebras can be very different from the theory of complex Banach algebras.

This correspondence between Lie groups and Lie algebras allows one to study Lie groups in terms of Lie algebras.

Advertentie

These phrases have their own page with example sentences containing the full combination:

Common combinations with algebras

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "algebras" in a sentence?
An example: "There exists some structure theory for such algebras that generalizes the analogous results for Lie algebras and associative algebras." This page contains 10+ example sentences with the word "algebras" from authentic English texts.
What does "algebras" mean?
Algebras means: plural of algebra
How many example sentences with "algebras" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "algebras", drawn from a database of millions of English sentences.