5.3 Applications to Algebra
Applications of compactness and Lowenheim Skolem to algebraic structures and existence results.
Tag
Algebra
14 notes
5.2 Algebraic Abstraction
Replacing concrete values with symbols and rules to express general patterns.
4.5 Examples Across Algebra and Geometry
Examples of first order structures from algebra, order theory, graph theory, and geometry.
20. Group Theory and Generalizations
This volume studies groups as algebraic structures encoding symmetry.
19. K-Theory
This volume studies algebraic and topological K-theory, focusing on invariants derived from vector bundles, modules, and operator algebras.
17. Non-Associative Rings and Algebras
This volume studies algebraic systems where associativity does not hold in general.
16. Associative Rings and Algebras
This volume studies rings and algebras with associative multiplication, without requiring commutativity.
15. Linear and Multilinear Algebra; Matrix Theory
This volume develops vector spaces, linear maps, matrices, and multilinear structures.
14. Algebraic Geometry
This volume studies geometric objects defined by polynomial equations.
13. Commutative Algebra
This volume studies commutative rings, ideals, modules, and their structural properties.
12. Field Theory and Polynomials
This volume studies fields, polynomials, and algebraic extensions.
11. Number Theory
Integers, primes, modular arithmetic, Diophantine equations, and modern analytic and algebraic methods.
08. General Algebraic Systems
Operations, identities, and structures as a unifying framework for all algebraic theories.
06. Order and Lattices
Partially ordered sets, lattices, and algebraic systems equipped with order relations.