相对于余挠对的强Gorenstein内射模

Strongly Gorenstein injective modules with respect to a cotorsion pair

作为强Gorenstein内射模的推广,文中引入了相对于完备遗传余挠对(X,Y)的强Gorenstein内射模,即强Gorenstein(X∩Y,Y)-内射模,并给出了等价刻画和若干性质,而且还研究了强Gorenstein(X∩Y,Y)-内射模的稳定性,讨论了与Gorenstein(X∩Y,Y)-内射模之间的关系。

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.