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- Title
An alternative perspective on flatness of modules.
- Authors
Durğun, Yılmaz
- Abstract
Given modules and , is said to be absolutely -pure if is a monomorphism for every extension of . For a module , the absolutely pure domain of is defined to be the collection of all modules such that is absolutely -pure. As an opposite to flatness, a module is said to be f-indigent if its absolutely pure domain is smallest possible, namely, consisting of exactly the fp-injective modules. Properties of absolutely pure domains and off-indigent modules are studied. In particular, the existence of f-indigent modules is determined for an arbitrary rings. For various classes of modules (such as finitely generated, simple, singular), necessary and sufficient conditions for the existence of f-indigent modules of those types are studied. Furthermore, f-indigent modules on commutative Noetherian hereditary rings are characterized.
- Subjects
FLATNESS measurement; MODULES (Algebra); NOETHERIAN rings; QUASI-Frobenius rings; FROBENIUS algebras
- Publication
Journal of Algebra & Its Applications, 2016, Vol 15, Issue 8, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498816501450