Krull Dimension and Classical Krull Dimension of Modules

Jaime Castro Pérez, José Ríos Montes
2014 Communications in Algebra  
We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula-plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-companion is strongly minimal. We also prove that the length of any increasing sequence of prime types is
more » ... bounded, so every formula has finite Krull dimension.
doi:10.1080/00927872.2013.781611 fatcat:nd6hkq7llzecre4p5x2rdt3pby