Related papers: The M-Principal Graph of a Commutative Ring

This paper has been withdrawn by the authors due to several major changes in concepts and results. New version will follow briefly as a new e-print.

This paper has been withdrawn by the author because overcame by arXiv:0910.4694

This paper has been withdrawn by the author.

This paper has been withdrawn by the author, due a critical mistake on page 3.

This paper has been withdrawn.

This paper has been withdrawn.

This paper has been withdrawn by the authors due to a mistake in the proof of Theorem 1.

This article is withdrawn because of a mistake in the main result of the paper.

This paper has been withdrawn by the author due to the gaps in the proofs of Proposition 2.2 and Proposition 3.2

This paper has been withdrawn.

This paper has been withdrawn by the author due to incomplete interpretation for the results.

This paper has been withdrawn by the author due to a crucial error in one of equation in (3).

This paper is withdrawn.

This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.

This paper has been withdrawn by the author due to a crucial error in last part of proof.

This paper has been temporarily withdrawn for corrections.

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the author due to an error in the proof of Proposition 4.8.

This paper has been withdrawn due to an error in the proof of the main theorem.

This paper has been withdrawn by the authors because the paper is largely revised and improved.