This thesis considers abstract algebra from a constructive point of view. The central concept of study is coherent rings − algebraic structures in which it is possible to solve homogeneous systems of linear equations. Three different algebraic theories are considered; Bézout domains, Prüfer domains and polynomial rings. The first two of these are non-Noetherian analogues of classical notions. T...

We begin this paper with a discussion of n-dimensional algebraic Vector bundles. Vector bundles of rank n may be identified with locally free Ox-modules of rank n. Several sections are dedicated to reviewing the basic notions of scheme-theory. We show how to construct the projectization of arbitrary rings. This construction corresponds to the construction of the tautological line bundle over an...

We compute the Gorenstein weak dimension of a coherent power series rings over a commutative rings and we show that, in general, Gwdim (R) ≤ 1 does not imply that R is an arithmetical ring.