Some articles on nonzero:

Structure Theorem For Finitely Generated Modules Over A Principal Ideal Domain - Statement - Invariant Factor Decomposition
... The order of the nonzero ideals is invariant, and the number of is invariant ... The nonzero elements, together with the number of which are zero, form a complete set of invariants for the module ... the free part of M separately where the visible are nonzero, and f is the number of 's which are 0 ...
Spectral Theory Of Compact Operators - Compact Operators - Statement
... i) Every nonzero λ ∈ σ(C) is an eigenvalue of C ... ii) For all nonzero λ ∈ σ(C), there exist m such that Ker(λi - A)m = Ker(λi - A)m+1, and this subspace is finite dimensional ... v) Every nonzero λ ∈ σ(C) is a pole of the resolvent function ζ → (ζ - C)−1 ...
Bézout's Identity - Proof
... Euclidean division defining property, namely that the division by a nonzero integer b has a remainder strictly less than