Abstract

Ordinary commutative algebraic geometry is based on commutative polynomial algebras over an algebraically closed eld k. Here we make a natural generalization to matrix polynomial k-algebras which are non-commutative coordinate rings of non-commutative varieties

Highlights

  • In the Zariski topology, we have the definition of regular functions: Let U ⊆ n be an open subset

  • Commutative affine algebraic geometry, the basic object is the polynomial algebra in d Є N variables

  • The generalized concept of localization immediately gives the natural generalizations of affine varieties, regular maps, and morphisms

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Summary

Introduction

In the Zariski topology, we have the definition of regular functions: Let U ⊆ n be an open subset. B) An Inductive system is the dual of a projective: It is a family of objects {Ai}i∈I together with transition morphisms ψ ij : Ai → Aj for each pair i ≤ j ∈ I with the properties that, for each i ∈ I ,ψ ii = id and if i ≤ j ≤ k ψ jk °ψ ij = ψ ik . Morphism between two affine varieties V,W is a continuous map φ :V → W such that the induced map φ # : W (U ) → V (φ −1(U )) is well defined for each open U ⊆ W , that is f f °φ is regular on V.

Results
Conclusion

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