Modules over Non-Noetherian Domains

Some model theory of modules over Bézout domains. The width

“…However, because our analysis depends only on Γ(B), this is a problem of the theory of lattice ordered abelian groups, which are classified (see [1,Sec. 3.4]).…”

“…Clearly Γ + (B) is a non-negative part of the value group of B, which is an abelian lattice ordered group (see [1,Sec. 3.5] for more on that).…”

“…3.5] for more on that). Furthermore, the famous Kaplansky-Jaffard-Ohm theorem (see [1,Thm. 3.5.3]) says that every lattice ordered abelian groups occurs as a value group of some Bézout domain B.…”

Does Int $${(\mathbb {Z})}$$ have the stacked bases property?

“…We have just said that the stacked bases property implies the UCS-property. The converse holds for Prüfer domains: Proposition 2.3 [1] (see also [6,Thm 4.8…”

Cotorsion pairs generated by modules of bounded projective dimension

“…To this regard we recall the following results. [21,VI 6] it is proved that every module in P 1 admits a filtration consisting of countably generated submodules of projective dimension at most one. Hence the cotorsion pair (P 1 , P ⊥ 1 ) is of countable type.…”