Can we classify modules as stated in the title:
Free module,
Module has torsion,
Module is neihter free nor has torsion?
In addition, lets say I have a module generated by $\{A, B\}$ over the ring of Laurent polynomials $R = \mathbb{Z}[x,x^{-1}]$.
Case 1:
If the module has a relation $B = x^2B$...In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Artin (1969, 1971) for use in deformation theory. Intuitively,
schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces are given by gluing together affine schemes using the finer étale topology. Alternatively one can think of schemes as being locally isomorphic to affine schemes in the Zariski topology, while algebraic spaces are locally isomorphic to affine schemes in the étale topology.
The resulting category of algebraic spaces extends the...
If X is a quasi-separated algebraic space and Spec k -> X is an etale presentation, then X is isomorphic to Spec k' for a field k'. (This is also true if X is Zariski locally quasi-separated.) The examples of algebraic spaces I know where this fails have diagonals that are not immersions.
Is t...
