Commutative Algebra I
A commutative ring is a field if for all non-zero elements r ? R, there exits r ? R (denoted r?1) such that rr = 1. Example 1. The integers, Z, and the fields Q ...
Homomorphisms of algebraic groups: representability and rigidityAbstract. Given two algebraic groups G, H over a field k, we investigate the representability of the functor of morphisms (of schemes) Hom(G, H). ?-rings: Definitions and basic properties... rings . . . . . . 77. 9.4. Adams operations are ring homomorphisms when the ?-ring is special . 81. 9.5. The equality e?T (x) = ?T · d. dT log ... Homological Algebra IIFor example, td(Z) = 1 since fd(Z2) = 1 and for any Z-module A ... Let ZG be the group ring of G over Z. Thus ZG is the free abelian ...
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