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tensor ring
Contents
Context
Algebra
algebra , higher algebra
universal algebra
monoid , semigroup , quasigroup
nonassociative algebra
associative unital algebra
commutative algebra
Lie algebra , Jordan algebra
Leibniz algebra , pre-Lie algebra
Poisson algebra , Frobenius algebra
lattice , frame , quantale
Boolean ring , Heyting algebra
commutator , center
monad , comonad
distributive law
Group theory
Ring theory
Module theory
Group theory
group theory
Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
Contents
Idea
A free monoid object in Ab
Definition
Given an abelian group G G , the tensor ring is a ring T ( G ) T(G) with an abelian group homomorphism g : G → T ( G ) g:G \to T(G) , such that for every other ring R R with abelian group homomorphism h : G → R h:G \to R , there is a unique ring homomorphism i : T ( G ) → R i:T(G) \to R such that i ∘ g = h i \circ g = h .
See also
Last revised on August 19, 2024 at 15:26:56.
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