Homological dimension, the Glossary

Table of Contents

1. 6 relations: Cohomological dimension, Global dimension, Homological algebra, Injective module, Projective module, Weak dimension.

2. Set index articles on mathematics

Cohomological dimension

In abstract algebra, cohomological dimension is an invariant of a group which measures the homological complexity of its representations. Homological dimension and cohomological dimension are homological algebra.

See Homological dimension and Cohomological dimension

Global dimension

In ring theory and homological algebra, the global dimension (or global homological dimension; sometimes just called homological dimension) of a ring A denoted gl dim A, is a non-negative integer or infinity which is a homological invariant of the ring. Homological dimension and global dimension are homological algebra.

See Homological dimension and Global dimension

Homological algebra

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting.

See Homological dimension and Homological algebra

Injective module

In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Homological dimension and injective module are homological algebra.

See Homological dimension and Injective module

Projective module

In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, keeping some of the main properties of free modules. Homological dimension and projective module are homological algebra.

See Homological dimension and Projective module

Weak dimension

In abstract algebra, the weak dimension of a nonzero right module M over a ring R is the largest number n such that the Tor group \operatorname_n^R(M,N) is nonzero for some left R-module N (or infinity if no largest such n exists), and the weak dimension of a left R-module is defined similarly. Homological dimension and weak dimension are homological algebra.

See Homological dimension and Weak dimension

See also

Set index articles on mathematics

• Ε-net
• Ξ function
• Adjoint
• Apeirogonal tiling
• Axiom of countability
• Baumgartner's axiom
• Boolean-valued
• Cartan's lemma
• Characteristic function
• Comparison theorem
• Compound of cubes
• Compound of octahedra
• Compound of tetrahedra
• Confocal
• Cyclic (mathematics)
• Dehn plane
• Differential (mathematics)
• Error term
• Euler integral
• Facet (geometry)
• Fermat's theorem
• Graded structure
• Harmonic (mathematics)
• Homological dimension
• Irreducibility (mathematics)
• Janko group
• Negative definiteness
• Noetherian
• Order (mathematics)
• P-adic cohomology
• Positive definiteness
• Quasiperiodic tiling
• Separation theorem
• Socle (mathematics)
• Stationary distribution
• Stratification (mathematics)
• Strong topology
• Supersingular variety
• Symbol (number theory)
• Uniqueness theorem
• Vector multiplication
• Vorlesungen über Zahlentheorie
• Zero–one law

References

[1] https://en.wikipedia.org/wiki/Homological_dimension

Also known as Homological dimension (disambiguation).