On P-extending modules.
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Let A be an artin algebra over a commutative artin ring R and ind A the category of indecomposable finitely generated right A-modules. Denote to be the full subcategory of ind A formed by the modules X whose all predecessors in ind A have projective dimension at most one, and by the full subcategory of ind A formed by the modules X whose all successors in ind A have injective dimension at most one. Recently, two classes of artin algebras A with co-finite in ind A, quasi-tilted...