Normally flat ring

In algebraic geometry, a normally flat ring along a proper ideal I is a local ring A such that I^n/I^ is flat over A/I for each integer n \ge 0. ^[1]

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Table of Contents

1. 5 relations: Alexander Grothendieck, Algebraic geometry, Flat module, Local ring, Resolution of singularities.

Alexander Grothendieck

Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born mathematician who became the leading figure in the creation of modern algebraic geometry.

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Algebraic geometry

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.

See Normally flat ring and Algebraic geometry

Flat module

In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion free modules. Normally flat ring and flat module are algebraic geometry.

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Local ring

In mathematics, more specifically in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on algebraic varieties or manifolds, or of algebraic number fields examined at a particular place, or prime.

See Normally flat ring and Local ring

Resolution of singularities

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. Normally flat ring and resolution of singularities are algebraic geometry.

See Normally flat ring and Resolution of singularities

References

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

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