JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (8): 102-107.doi: 10.6040/j.issn.1671-9352.0.2018.517

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Strongly Gorenstein injective modules with respect to a cotorsion pair

WANG Zhan-ping, YUAN Kai-ying   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Online:2019-08-20 Published:2019-07-03

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Abstract: As a generalization of strongly Gorenstein injective modules, this paper introduces and studys strongly Gorenstein injective modules with respect to a complete and hereditary cotorsion pair(X,Y), that is, strongly Gorenstein(X∩Y,Y)-injective modules, and give some properties and equivalent characterizations. Moreover, the stability of strongly Gorenstein(X∩Y,Y)-injective modules is studied, and the relation between it and Gorenstein(X∩Y,Y)-injective modules is discussed.

Key words: cotorsion pair, Gorenstein(X∩Y,Y)-injective module, strongly Gorenstein(X∩Y,Y)-injective module, stability

CLC Number: 

  • O153.3
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