The existence of relative pure injective envelopes

• Autorzy: Fatemeh Zareh-Khoshchehreh , Kamran Divaani-Aazar
• Języki publikacji: EN

Abstrakty

EN

Let 𝓢 be a class of finitely presented R-modules such that R∈ 𝓢 and 𝓢 has a subset 𝓢* with the property that for any U∈ 𝓢 there is a U*∈ 𝓢* with U* ≅ U. We show that the class of 𝓢-pure injective R-modules is preenveloping. As an application, we deduce that the left global 𝓢-pure projective dimension of R is equal to its left global 𝓢-pure injective dimension. As our main result, we prove that, in fact, the class of 𝓢-pure injective R-modules is enveloping.

Kategorie tematyczne

• 16D10: General module theory
• 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 130
• Numer: 2
• Strony: 251-264

Daty

wydano

2013

Twórcy

autor

Fatemeh Zareh-Khoshchehreh

• Department of Mathematics, Alzahra University, Vanak, Post Code 19834, Tehran, Iran

autor

Kamran Divaani-Aazar

• Department of Mathematics, Alzahra University, Vanak, Post Code 19834, Tehran, Iran
• Institute for Studies, in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran

Identyfikatory

DOI

10.4064/cm130-2-7