On f-injective modules |
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Authors: | M. Zayed |
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Affiliation: | Department of Mathematics, Faculty of Science, University of Banha, Banha 13518, Egypt, EG
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Abstract: | In this paper, the notions of f-injective and f*-injective modules are introduced. Elementary properties of these modules are given. For instance, a ring R is coherent iff any ultraproduct of f-injective modules is absolutely pure. We prove that the class S* Sigma^* of f*-injective modules is closed under ultraproducts. On the other hand, S* Sigma^* is not axiomatisable. For coherent rings R, S* Sigma^* is axiomatisable iff every c0 chi_0 -injective module is f*-injective. Further, it is shown that the class S Sigma of f-injective modules is axiomatisable iff R is coherent and every c0 chi_0 -injective module is f-injective. Finally, an f-injective module H, such that every module embeds in an ultraprower of H, is given. |
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