Finitely presented and coherent ordered modules and rings

摘要

We extend the usual definition of coherence, for modules over rings, to partially ordered right modules over a large class of partially ordered rings, calledpo-rings. In this situation, coherence is equivalent to saying that solution sets of finite systems of inequalities are finitely generated semimodules. Coherence for ordered rings and modules, which we callpo-coherence, has the following features:.