Remarks on f p-Injective and f p-Flat Modules.
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| Title: | Remarks on f p-Injective and f p-Flat Modules. |
|---|---|
| Authors: | Mao, Lixin1 maolx2@hotmail.com |
| Source: | Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ). Oct2011, Vol. 36 Issue 6, p1013-1022. 10p. |
| Subjects: | Injective modules (Algebra), Algebraic topology, Ring theory, Finite groups, Frobenius algebras, Associative rings |
| Abstract (English): | A left R-module M is said to be f p-injective if, for every monomorphism K → L with K and L finitely presented left R-modules, Hom( L, M) → Hom( K, M) is an epimorphism. A right R-module N is called f p-flat if, for every monomorphism K → L with K and L finitely presented left R-modules, $${N\otimes K\rightarrow N\otimes L}$$ is a monomorphism. In this note, we study precovers and preenvelopes by f p-injective and f p-flat modules, including their properties under (almost) excellent extensions of rings. In addition, we also introduce and investigate f p-projective modules. [ABSTRACT FROM AUTHOR] |
| Abstract (Arabic): | [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR] |
| Copyright of Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 66143119 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Remarks on f p-Injective and f p-Flat Modules. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Mao%2C+Lixin%22">Mao, Lixin</searchLink><relatesTo>1</relatesTo><i> maolx2@hotmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Arabian+Journal+for+Science+%26+Engineering+%28Springer+Science+%26+Business+Media+B%2EV%2E+%29%22">Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. )</searchLink>. Oct2011, Vol. 36 Issue 6, p1013-1022. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Injective+modules+%28Algebra%29%22">Injective modules (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+topology%22">Algebraic topology</searchLink><br /><searchLink fieldCode="DE" term="%22Ring+theory%22">Ring theory</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+groups%22">Finite groups</searchLink><br /><searchLink fieldCode="DE" term="%22Frobenius+algebras%22">Frobenius algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Associative+rings%22">Associative rings</searchLink> – Name: Abstract Label: Abstract (English) Group: Ab Data: A left R-module M is said to be f p-injective if, for every monomorphism K → L with K and L finitely presented left R-modules, Hom( L, M) → Hom( K, M) is an epimorphism. A right R-module N is called f p-flat if, for every monomorphism K → L with K and L finitely presented left R-modules, $${N\otimes K\rightarrow N\otimes L}$$ is a monomorphism. In this note, we study precovers and preenvelopes by f p-injective and f p-flat modules, including their properties under (almost) excellent extensions of rings. In addition, we also introduce and investigate f p-projective modules. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Abstract (Arabic) Group: Ab Data: [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s13369-011-0050-z Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 1013 Subjects: – SubjectFull: Injective modules (Algebra) Type: general – SubjectFull: Algebraic topology Type: general – SubjectFull: Ring theory Type: general – SubjectFull: Finite groups Type: general – SubjectFull: Frobenius algebras Type: general – SubjectFull: Associative rings Type: general Titles: – TitleFull: Remarks on f p-Injective and f p-Flat Modules. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Mao, Lixin IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2011 Type: published Y: 2011 Identifiers: – Type: issn-print Value: 2193567X Numbering: – Type: volume Value: 36 – Type: issue Value: 6 Titles: – TitleFull: Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ) Type: main |
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