Commutative affine rings

1999 ◽  
Vol 40 (1) ◽  
pp. 3-8 ◽  
Author(s):  
I. Kh. Bekker
Keyword(s):  
Affine Rings

Affine rings of dimension one

1972 ◽  
Vol 13 (1) ◽  
pp. 155-156 ◽  
Author(s):  
V. T. Markov
Keyword(s):  
Affine Rings ◽  
Dimension One

Generators and relations for the affine rings of the classical groups

1992 ◽  
Vol 20 (10) ◽  
pp. 2877-2902 ◽  
Author(s):  
Daniel E. Plath ◽  
Jacob Towber
Keyword(s):  
Classical Groups ◽  
Generators And Relations ◽  
Affine Rings

scholarly journals Some remarks on affine rings

1986 ◽  
Vol 98 (4) ◽  
pp. 537-537 ◽  
Author(s):  
S. Montgomery ◽  
L. W. Small
Keyword(s):  
Affine Rings

Basic Objects for an Algebraic Homotopy Theory

1972 ◽  
Vol 24 (1) ◽  
pp. 155-166 ◽  
Author(s):  
Paul Cherenack
Keyword(s):  
Homotopy Theory ◽  
Galois Theory ◽  
Point Of View ◽  
Geometric Point ◽  
Algebraic Loop ◽  
Affine Rings ◽  
Algebraic Homotopy Theory

The purposes of this paper are:(A) To show (§§ 1, 3, 5) that some of the usual notions of homotopy theory (sums, quotients, suspensions, loop functors) exist in the category of affine k-schemes where the affine rings are countably generated.(B) By example to demonstrate some of the more geometric relations between two objects of and their quotient or to study the algebraic suspension of one of them. See §§ 2.1, 2.2, 2.3, 3.(C) To prove (§4) that the algebraic suspension (in R/) of the n-sphere is homeomorphic to the n + 1 sphere for the usual topologies.(D) To show that the algebraic loop functor is right adjoint to the algebraic suspension functor (§5).These results can be viewed as a precursor of definitions for an algebraic homotopy theory from a “geometric” point of view (rather than a more algebraic standpoint employing Galois theory [5]).

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