Abstract

Let T⁎ be the theory of lattice-ordered, convex subrings of von Neumann regular real closed rings that are divisible-projectable, sc-regular ([12]) and have no minimal (non zero) idempotents. In this paper, we introduce and study a local divisibility binary relation that, added to the language for lattice-ordered rings, together with the (usual) divisibility relation and the radical relation associated to the minimal prime spectrum ([19]) yields quantifier elimination for T⁎.

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