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We show that the ring of locally bounded Nash meromorphic functions on a connected d-dimensional Nash submanifold of R" is a Priifer domain and every finitely generated ideal in this ring can be generated by d -f 1 elements. Moreover, every finitely generated ideal can be generated by d elements if and only if the Nash manifold is noncompact.doi:10.1017/s0004972700021912 fatcat:mm6q5i4gmfgihoq34vliioawdi