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  1. 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. [100%] 2023-12-31 [Mathematical logic]
  2. 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. [100%] 2023-12-31 [Mathematical logic]
  3. Linear algebraic groups, arithmetic theory of: The theory that studies arithmetic properties of linear algebraic groups (cf. Linear algebraic group), defined, as a rule, over a global field. (Mathematics) [95%] 2023-12-18
  4. Algebraic algebra: An algebra with associative powers (in particular, an associative algebra) over a field in which all elements are algebraic: an element $a$ of the algebra $A$ is called algebraic over the field $F$ if the subalgebra $F$ generated by $a ... (Mathematics) [92%] 2023-10-13
  5. 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) [88%] 2023-12-31 [Algebraic K-theory] [Theorems in algebraic topology]...
  6. Algebraic group: In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. (Algebraic variety with a group structure) [88%] 2023-12-19 [Algebraic groups] [Properties of groups]...
  7. Algebraic group: A group $G$ provided with the structure of an algebraic variety in which the multiplication $ \mu: G\times G \to G $ and the inversion mapping $\nu: G \to G$ are regular mappings (morphisms) of algebraic varieties. An algebraic group is ... (Mathematics) [88%] 2023-12-15
  8. Automata, algebraic theory of: A branch of the theory of automata (cf. Automata, theory of) in which algebraic tools are employed in the study of automata. (Mathematics) [87%] 2023-12-31
  9. Lie algebra of an algebraic group: l0584801.png ~/encyclopedia/old_files/data/L058/L.0508480 104 0 104 The analogue of the Lie algebra of an analytic group, which relates to the case of affine algebraic groups. As in the analytic case, the Lie algebra of an ... (Mathematics) [86%] 2023-12-15
  10. Algebraic K-theory: Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. [81%] 2024-01-09 [Algebraic K-theory] [Algebraic geometry]...
  11. Algebraic K-theory: A branch of algebra, dealing mainly with the study of the so-called $K$-functors ($K_0, K_1$, etc., cf. $K$-functor); it is a part of general linear algebra. (Mathematics) [81%] 2024-01-09
  12. 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) [81%] 2023-12-13
  13. Algebraic graph theory: Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. (Branch of mathematics) [81%] 2024-08-28 [Algebraic graph theory]
  14. 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) [81%] 2024-07-18 [Algebraic number theory] [Number theory]...
  15. Algebraic graph theory: Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. (Branch of mathematics) [81%] 2024-10-16 [Algebraic graph theory]
  16. Group theory: In mathematics, groups often arise as structures representing the set of possible symmetries of some object. We have been intentionally vague about the meaning of the terms symmetry and object. [79%] 2023-06-26
  17. Group theory: Group theory is the study of mathematical groups, including their symmetries and permutations. It has applications in science, and has become one of the most active branches in all of mathematics in the 20th century. [79%] 2023-03-13 [Algebra]
  18. Group theory: Welcome to Group Theory! Group Theory is a vibrant, wide area of current research in mathematics, computer science and mathematical/theoretical physics. [79%] 2024-01-19 [{{PAGENAME}}]
  19. Group theory: In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups ... (Branch of mathematics that studies the properties of groups) [79%] 2024-08-13 [Group theory]
  20. Theory of Lie groups: In mathematics, Theory of Lie groups is a series of books on Lie groups by Claude Chevalley (1946, 1951, 1955). The first in the series was one of the earliest books on Lie groups to treat them from the global ... [79%] 2023-10-08 [Mathematics books] [Lie groups]...

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