The Equivalence of Tight and Essentially Tight Modules Under Specific Conditions
Tight and essentially tight modules, generalizations of weakly injective modules, are equivalent under specific conditions, including when the module is uniform, its injective hull is a direct sum of indecomposables, the ring is q.f.d., or the module is nonsingular over a semiprime Goldie ring.
Non-injective Inductions and Restrictions of Modules over Finite Groups: Extending Classical Results
This note generalizes the concepts of induction and restriction of modules over finite groups to non-injective group homomorphisms, proving key properties like transitivity, Frobenius reciprocity, and Mackey's formula in this extended context.
On the Freeness and Rank of Duals of Free Modules over Noetherian Commutative Rings
This research paper investigates the conditions under which the dual of a free module over a Noetherian commutative ring is itself free, focusing on the role of the ring's properties (like being Artinian or slender) and cardinalities of the module and the ring.
Strong Purity and Phantom Morphisms in Module Theory
This research paper explores the concepts of S-purity and S-phantom morphisms in module theory, demonstrating their properties and relationships to other module classes, particularly under the conditions of the Optimistic Conjecture.
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