| The work in this thesis is motivated by an approach to trying to understand the K-theory of fields. The calculation of cohomology algebras undertaken here will hopefully give some insight into a relationship between the K-theory of an arbitrary field and that of its algebraic closure.;The calculation involves building resolutions over the rings in question, and then finding chain maps that correspond to elements of the algebra to allow for the determination of the Yoneda pairing. Because of the intractability of the latter in many cases, a spectral sequence is employed to reduce this to a calculation in low degrees, which is then done explicitly.;This spectral sequence approach to calculating the product structure does not work for a more general case because of the reduced symmetry. It is hoped that a map from the rings in question into simpler rings will give rise to a map on the level of cohomology algebras that will allow for the determination of the product structure in this and possibly more general cases. |
