Algebras example sentences

"Algebras" Example Sentences

1. There are different types of algebras used in mathematics.
2. The study of algebras requires a strong foundation in arithmetic.
3. Modern algebraic structures incorporate Boolean algebras and other concepts.
4. Algebras can be used to model real-world systems.
5. A commutative algebra is one in which the order of the operands does not matter.
6. Linear algebras are used in physics and engineering.
7. A homomorphic algebraic system allows for consistent arithmetic operations across domains.
8. The distributive property is a fundamental concept in most algebras.
9. The algebraic theory of numbers investigates the properties of integers and rational numbers.
10. Boolean algebras are used in computer science to represent logical circuits.
11. Lie algebras are a type of algebra used in group theory.
12. The algebraic definition of a vector space involves closure under addition and scalar multiplication.
13. A non-associative algebra is one in which the order of the operands matters.
14. Algebraic geometry studies the intersection of algebra and geometry.
15. The algebra of polynomials is a basic domain in abstract algebra.
16. A linear associative algebra is defined by the associative property of multiplication.
17. Commutative algebras find applications in algebraic coding theory.
18. Homological algebra is used to study algebraic structures via their abstract properties.
19. A non-commutative algebra is one in which the order of the operands matters.
20. Algebraic structures can be used to analyze and optimize computer algorithms.
21. The zero element is an essential concept in most algebras.
22. Galois theory investigates the properties of algebraic fields via their symmetries.
23. A free algebra is one generated from a given set of generators and relations.
24. The classification of finite simple groups is a problem in algebraic group theory.
25. A boolean algebra is a type of algebra with two values, true and false.
26. The Brauer group is a key concept in algebraic number theory.
27. Modular forms are used in number theory and algebraic geometry.
28. A graded algebra involves elements of different "degrees" or "levels".
29. The notion of an algebra over a ring generalizes the concept of a vector space.
30. The alternating group is an important algebraic structure in group theory.

Common Phases

1. Linear algebras; abstract algebras; commutative algebras; non-commutative algebras.
2. Boolean algebras; lattice algebras; Heyting algebras; propositional algebras.
3. Matrix algebras; polynomial algebras; group algebras; Lie algebras.
4. Universal algebras; module algebras; differential algebras; Hopf algebras.
5. Ordered algebras; graded algebras; associative algebras; non-associative algebras.