Theorems · Definition · ring theory
TrivSqZeroExt
Type u → Type v → Type (max u v)
"Trivial Square-Zero Extension".
Given a module M over a ring R, the trivial square-zero extension of M over R is defined
to be the R-algebra R × M with multiplication given by
(r₁ + m₁) * (r₂ + m₂) = r₁ r₂ + r₁ m₂ + r₂ m₁.
It is a square-zero extension because M^2 = 0.
- Defined in
- Mathlib.Algebra.TrivSqZeroExt.Basic
- Cited by
- 180 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
Around this declaration
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Cites0
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Nothing in Mathlib beyond the foundations.
Cited by205
Results whose statement or proof uses this declaration.
- TrivSqZeroExt.fststatement and proof · cited by 96
- TrivSqZeroExt.sndstatement and proof · cited by 83
- TrivSqZeroExt.inlstatement · cited by 64
- TrivSqZeroExt.inrstatement · cited by 59
- DualNumberproof · cited by 52
- TrivSqZeroExt.extstatement and proof · cited by 29
- TrivSqZeroExt.inlAlgHomstatement · cited by 17
- TrivSqZeroExt.inrHomstatement · cited by 16
- TrivSqZeroExt.mapstatement · cited by 12
- TrivSqZeroExt.liftstatement · cited by 10
- TrivSqZeroExt.sndHomstatement · cited by 6
- ExteriorAlgebra.toTrivSqZeroExtstatement · cited by 5
Showing the 200 most cited of 205.