Publication Date:
2018-03-06

Description:
Let R be a ring. A subclass T of left R -modules is called a weak torsion class if it is closed under homomorphic images and extensions. Let T be a weak torsion class of left R -modules and n a positive integer. Then a left R -module M is called T -finitely generated if there exists a finitely generated submodule N such that M/N ∈ T ; a left R -module A is called ( T , n )-presented if there exists an exact sequence of left R -modules $$0 \to K_{n - 1} \to F_{n - 1} \to \ldots \to F_1 \to F_0 \to M \to 0$$ such that F 0 ,..., F n -1 are finitely generated free and K n -1 is T -finitely generated; a left R -module M is called ( T , n )-injective, if Ext R n ( A,M ) = 0 for each ( T , n +1)-presented left R -module A ; a right R -module M is called ( T , n )-flat, if Tor n R ( M,A ) = 0 for each ( T , n +1)-presented left R -module A . A ring R is called ( T , n )-coherent, if every ( T , n +1)-presented module is ( n + 1)-presented. Some characterizations and properties of these modules and rings are given.

Print ISSN:
0011-4642

Electronic ISSN:
1572-9141

Topics:
Mathematics

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