Pure Baer injective modules
In this paper we generalize the notion of pure injectivity of modules by introducing what we call a pure Baer injective module. Some properties and some characterization of such modules are established. We also introduce two notions closely related to pure Baer injectivity; namely, the notions of a...
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000720 |
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| _version_ | 1850237436546777088 |
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| author | Nada M. Al Thani |
| author_facet | Nada M. Al Thani |
| author_sort | Nada M. Al Thani |
| collection | DOAJ |
| description | In this paper we generalize the notion of pure injectivity of modules by introducing what
we call a pure Baer injective module. Some properties and some characterization of such modules are
established. We also introduce two notions closely related to pure Baer injectivity; namely, the notions of
a ∑-pure Baer injective module and that of SSBI-ring. A ring R is an SSBI-ring if and only if every
smisimple R-module is pure Baer injective. To investigate such algebraic structures we had to define
what we call p-essential extension modules, pure relative complement submodules, left pure hereditary
rings and some other related notions. The basic properties of these concepts and their interrelationships
are explored, and are further related to the notions of pure split modules. |
| format | Article |
| id | doaj-art-1d2d1185b5f14e06b4c21fa0af2d101c |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1d2d1185b5f14e06b4c21fa0af2d101c2025-08-20T02:01:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120352953810.1155/S0161171297000720Pure Baer injective modulesNada M. Al Thani0Department of Mathematics, Faculty of Science, Qatar University, Doha, QatarIn this paper we generalize the notion of pure injectivity of modules by introducing what we call a pure Baer injective module. Some properties and some characterization of such modules are established. We also introduce two notions closely related to pure Baer injectivity; namely, the notions of a ∑-pure Baer injective module and that of SSBI-ring. A ring R is an SSBI-ring if and only if every smisimple R-module is pure Baer injective. To investigate such algebraic structures we had to define what we call p-essential extension modules, pure relative complement submodules, left pure hereditary rings and some other related notions. The basic properties of these concepts and their interrelationships are explored, and are further related to the notions of pure split modules.http://dx.doi.org/10.1155/S0161171297000720pure and ∑-pure Baer injective modulespure hereditary ringpure split moduleP-essential extension submodulepure relative complement submoduleSSBI-ring. |
| spellingShingle | Nada M. Al Thani Pure Baer injective modules International Journal of Mathematics and Mathematical Sciences pure and ∑-pure Baer injective modules pure hereditary ring pure split module P-essential extension submodule pure relative complement submodule SSBI-ring. |
| title | Pure Baer injective modules |
| title_full | Pure Baer injective modules |
| title_fullStr | Pure Baer injective modules |
| title_full_unstemmed | Pure Baer injective modules |
| title_short | Pure Baer injective modules |
| title_sort | pure baer injective modules |
| topic | pure and ∑-pure Baer injective modules pure hereditary ring pure split module P-essential extension submodule pure relative complement submodule SSBI-ring. |
| url | http://dx.doi.org/10.1155/S0161171297000720 |
| work_keys_str_mv | AT nadamalthani purebaerinjectivemodules |