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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) [86%] 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) [86%] 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) [86%] 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. Theorum: Theorum (rhymes with decorum, apparently) is a neologism proposed by Richard Dawkins in The Greatest Show on Earth to distinguish the scientific meaning of theory from the colloquial meaning. In most of the opening introduction to the show, he substitutes ... [81%] 2024-01-05 [Neologisms] [Language]...
17. 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]...
18. Fundamental theorem of ideal theory in number fields: . [79%] 2023-05-28
19. 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]
20. 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]...