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Cohomology and Free abelian group

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Cohomology and Free abelian group

Cohomology vs. Free abelian group

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex. In abstract algebra, a free abelian group or free Z-module is an abelian group with a basis.

Similarities between Cohomology and Free abelian group

Cohomology and Free abelian group have 18 things in common (in Unionpedia): Abelian group, Abstract algebra, Algebraic geometry, Algebraic topology, Chain (algebraic topology), Chain complex, Direct sum, Exact sequence, Finitely generated module, Free module, Homology (mathematics), Integer, Manifold, Module (mathematics), Simplicial complex, Singular homology, Solomon Lefschetz, Vector space.

Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

Abelian group and Cohomology · Abelian group and Free abelian group · See more »

Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

Abstract algebra and Cohomology · Abstract algebra and Free abelian group · See more »

Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

Algebraic geometry and Cohomology · Algebraic geometry and Free abelian group · See more »

Algebraic topology

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.

Algebraic topology and Cohomology · Algebraic topology and Free abelian group · See more »

Chain (algebraic topology)

In algebraic topology, a -chain is a formal linear combination of the -cells in a cell complex.

Chain (algebraic topology) and Cohomology · Chain (algebraic topology) and Free abelian group · See more »

Chain complex

In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next.

Chain complex and Cohomology · Chain complex and Free abelian group · See more »

Direct sum

The direct sum is an operation from abstract algebra, a branch of mathematics.

Cohomology and Direct sum · Direct sum and Free abelian group · See more »

Exact sequence

An exact sequence is a concept in mathematics, especially in group theory, ring and module theory, homological algebra, as well as in differential geometry.

Cohomology and Exact sequence · Exact sequence and Free abelian group · See more »

Finitely generated module

In mathematics, a finitely generated module is a module that has a finite generating set.

Cohomology and Finitely generated module · Finitely generated module and Free abelian group · See more »

Free module

In mathematics, a free module is a module that has a basis – that is, a generating set consisting of linearly independent elements.

Cohomology and Free module · Free abelian group and Free module · See more »

Homology (mathematics)

In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.

Cohomology and Homology (mathematics) · Free abelian group and Homology (mathematics) · See more »

Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

Cohomology and Integer · Free abelian group and Integer · See more »

Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

Cohomology and Manifold · Free abelian group and Manifold · See more »

Module (mathematics)

In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.

Cohomology and Module (mathematics) · Free abelian group and Module (mathematics) · See more »

Simplicial complex

In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).

Cohomology and Simplicial complex · Free abelian group and Simplicial complex · See more »

Singular homology

In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of algebraic invariants of a topological space X, the so-called homology groups H_n(X).

Cohomology and Singular homology · Free abelian group and Singular homology · See more »

Solomon Lefschetz

Solomon Lefschetz (Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.

Cohomology and Solomon Lefschetz · Free abelian group and Solomon Lefschetz · See more »

Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

Cohomology and Vector space · Free abelian group and Vector space · See more »

The list above answers the following questions

Cohomology and Free abelian group Comparison

Cohomology has 186 relations, while Free abelian group has 95. As they have in common 18, the Jaccard index is 6.41% = 18 / (186 + 95).

References

This article shows the relationship between Cohomology and Free abelian group. To access each article from which the information was extracted, please visit:

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