  The proofs of K. Oka's Coherence Theorems are based on Weierstrass'
Preparation (division) Theorem. Here we formulate and prove a Weak Coherence
Theorem without using Weierstrass' Preparation Theorem, but only with power
series expansions: The proof is almost of linear algebra. Nevertheless, this
simple Weak Coherence Theorem suffices to give other proofs of the
Approximation, Cousin I/II, and Levi's (Hartogs' Inverse) Problems even in
simpler ways than those known, as far as the domains are non-singular; they
constitute the main basic part of the theory of several complex variables.
  The new approach enables us to complete the proofs of those problems in quite
an elementary way without Weierstrass' Preparation Theorem or the cohomology
theory of Cartan--Serre, nor L2-dbar method of Hoermander.
