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1. Algebraic number theory: The branch of number theory with the basic aim of studying properties of algebraic integers in algebraic number fields $ K $ of finite degree over the field $ \mathbf Q $ of rational numbers (cf. Algebraic number). (Mathematics) [100%] 2023-12-13
2. Algebraic number theory: Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic ... (Branch of number theory) [100%] 2024-07-18 [Algebraic number theory] [Number theory]...
3. Algebraic number theory: Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic ... (Branch of number theory) [100%] 2025-01-25 [Algebraic number theory] [Number theory]...
4. Modulus in algebraic number theory: A formal product of places of an algebraic number field, also termed an extended ideal. It is used to encode ramification data for abelian extensions of a number field (cf Conductor of an Abelian extension). (Mathematics) [92%] 2023-12-03
5. Stability theorems in algebraic K-theory: Assertions on the invariance of the groups $ K _{i} (R) $ or their subgroups, given certain special extensions of the ground ring $ R $( see Algebraic $ K $- theory). The following are the best-known stability theorems. (Mathematics) [85%] 2023-10-13
6. Basic theorems in algebraic K-theory: In mathematics, there are several theorems basic to algebraic K-theory. Throughout, for simplicity, we assume when an exact category is a subcategory of another exact category, we mean it is strictly full subcategory (i.e., isomorphism-closed.) Additivity theorem ... (Four mathematical theorems) [85%] 2025-06-08 [Algebraic K-theory] [Theorems in algebraic topology]...
7. Basic theorems in algebraic K-theory: In mathematics, there are several theorems basic to algebraic K-theory. Throughout, for simplicity, we assume when an exact category is a subcategory of another exact category, we mean it is strictly full subcategory (i.e., isomorphism-closed). (Four mathematical theorems) [85%] 2026-04-29 [Algebraic K-theory] [Theorems in algebraic topology]...
8. Algebraic number: A complex (sometimes, real) number that is a root of a polynomial $$f(x)=a_nx^n+\dotsb+a_1x+a_0\label{1}\tag{1}$$ with rational coefficients, not all of which are zero. If $\alpha$ is an algebraic number, then, among ... (Mathematics) [84%] 2023-10-09 [Number theory]
9. Algebraic number: In mathematics, and more specifically—in number theory, an algebraic number is a complex number that is a root of a polynomial with rational coefficients. Real or complex numbers that are not algebraic are called transcendental numbers. [84%] 2023-06-13
10. Algebraic theory: Informally in mathematical logic, an algebraic theory is a theory that uses axioms stated entirely in terms of equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. [82%] 2023-12-31 [Mathematical logic]
11. Algebraic theory: Informally in mathematical logic, an algebraic theory is a theory that uses axioms stated entirely in terms of equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. [82%] 2023-12-31 [Mathematical logic]
12. Theorem: A theorem is a statement that can be proven via logic which generally stems from a collection of postulates or axioms. They have been in use since Euclidean geometry as the basis of geometrical facts. [82%] 2023-02-21 [Mathematics]
13. Theorem: In logic, a theorem is formally meant to be a formula that can be transformed by applying inferential rules to axioms in a deductive system. This formal notion of proofs in logic is crucial in fields such as proof theory ... [82%] 2023-02-03
14. Theorem: In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a ... (In mathematics, a statement that has been proved) [82%] 2023-09-23 [Theorems] [Logical consequence]...
15. Theorem: A mathematical statement whose truth has been established by means of a proof. The concept of a theorem developed and became more precise together with the concept of a mathematical proof. (Mathematics) [82%] 2023-10-18
16. Fundamental theorem of algebraic K-theory: In algebra, the fundamental theorem of algebraic K-theory describes the effects of changing the ring of K-groups from a ring R to \displaystyle{ R }[/math] or \displaystyle{ R[t, t^{-1}] }[/math]. The theorem was first proved by ... (On the effects of changing the ring of ''K''-groups) [81%] 2023-12-31 [Algebraic K-theory] [Theorems in algebraic topology]...
17. Fundamental theorem of ideal theory in number fields: . [79%] 2023-05-28
18. Prime Number Theorem: The Prime Number Theorem is one of the most famous theorems in mathematics. It states that the number of primes not exceeding n is asymptotic to , where log(n) is the logarithm of (n) to the base e. [79%] 2023-02-09 [Number Theory]
19. Odd number theorem: The odd number theorem is a theorem in strong gravitational lensing which comes directly from differential topology. The theorem states that the number of multiple images produced by a bounded transparent lens must be odd. (Physics) [79%] 2024-01-19 [Gravitational lensing] [Physics theorems]...
20. Prime Number Theorem: The list of prime numbers suggests that they thin out the further you go: 44% of the one-digit numbers are prime, but only 23% of the two-digit numbers and 16% of the three-digit numbers. The trial division ... [79%] 2023-10-17