When are IG-projective modules projective?
R. Luo, D.M. Jian
TL;DR
This paper characterizes when finitely generated IG-projective modules over commutative Noetherian local rings are projective, establishing that selforthogonality is the key criterion for projectivity.
Contribution
It provides a necessary and sufficient condition linking IG-projectivity and projectivity via selforthogonality in a specific algebraic setting.
Findings
Finitely generated IG-projective modules are projective iff selforthogonal.
Selforthogonality characterizes projectivity among IG-projective modules.
The result applies to modules over commutative Noetherian local rings.
Abstract
This paper concerns when a finitely generated IG-projective module is projective over commutative Noetherian local rings. We prove that a finitely generated IG-projective module is projective if and only if it is selforthogonal.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras