Finitely presented and coherent ordered modules and rings

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dc.creatorWehrung, Friedrich
dc.date2005-01-25
dc.date.accessioned2026-07-07T05:16:22Z
dc.date.available2026-07-07T05:16:22Z
dc.descriptionWe extend the usual definition of coherence, for modules over rings, to partially ordered right modules over a large class of partially ordered rings, called po-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 call po-coherence, has the following features: (i) Every subring of Q, and every totally ordered division ring, is po-coherent. (ii) For a partially ordered right module A over a po-coherent poring R, A is po-coherent if and only if A is a finitely presented R-module and A^+ is a finitely generated R^+-semimodule. (iii) Every finitely po-presented partially ordered right module over a right po-coherent po-ring is po-coherent. (iv) Every finitely presented abelian lattice-ordered group is po-coherent.
dc.identifierhttps://arxiv.org/abs/math/0501433
dc.identifierhttp://arxiv.org/abs/math/0501433
dc.identifierCommunications in Algebra 27, no. 12 (1999) 5893--5919
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73960
dc.subjectGeneral Mathematics
dc.subject06F25, 16W80, 12J15, 15A39, 08C15
dc.titleFinitely presented and coherent ordered modules and rings
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