1Department of Mathematics Alzahra University Vanak, Post Code 19834 Tehran, Iran 2Department of Mathematics Alzahra University Vanak, Post Code 19834 Tehran, Iran and Institute for Studies in Theoretical Physics and Mathematics P.O. Box 19395-5746 Tehran, Iran
Colloquium Mathematicum, Tome 130 (2013) no. 2, pp. 251-264
Let $\mathcal {S}$ be a class of finitely presented $R$-modules such that $R\in \mathcal {S}$ and $\mathcal {S}$ has a subset $\mathcal {S}^*$ with the property that for any $U\in \mathcal {S}$ there is a $U^*\in \mathcal {S}^*$ with $U^*\cong U.$ We show that the class of $\mathcal {S}$-pure injective $R$-modules is preenveloping. As an application, we deduce that the left global $\mathcal {S}$-pure projective dimension of $R$ is equal to its left global $\mathcal {S}$-pure injective dimension. As our main result, we prove that, in fact, the class of $\mathcal {S}$-pure injective $R$-modules is enveloping.
Keywords:
mathcal class finitely presented r modules mathcal mathcal has subset mathcal * property mathcal there * mathcal * * cong class mathcal pure injective r modules preenveloping application deduce global mathcal pure projective dimension equal its global mathcal pure injective dimension main result prove class mathcal pure injective r modules enveloping
1
Department of Mathematics Alzahra University Vanak, Post Code 19834 Tehran, Iran
2
Department of Mathematics Alzahra University Vanak, Post Code 19834 Tehran, Iran and Institute for Studies in Theoretical Physics and Mathematics P.O. Box 19395-5746 Tehran, Iran
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Fatemeh Zareh-Khoshchehreh; Kamran Divaani-Aazar. The existence of relative pure injective envelopes. Colloquium Mathematicum, Tome 130 (2013) no. 2, pp. 251-264. doi: 10.4064/cm130-2-7
