Elementary pseudoconcavity and fields of CR meromorphic functions

This paper is a continuation of an earlier paper of the same authors [Rend. Sem. Mat. Univ. Padova 111 (2004), 179--204; MR2076739 (2005j:32039)]. The purpose of this paper is to carry over the results about algebraic dependence, transcendence degree and related matters for the field ${\scr K}(M)$K(M) of CR meromorphic functions on $M$M from the compact case to the noncompact case. This is done by introducing the notion of "elementary pseudoconcavity'' on a smooth noncompact CR manifold of CR dimension $n$n and CR codimension $k$k, which is assumed to have a certain local extension property $E$E. The authors thus follow the ideas of Andreotti, who used a similar approach to generalize several results of Siegel about the field ${\scr K}(X)$K(X) of meromorphic functions on a compact complex manifold $X$X.