Bulletin of the
Korean Mathematical Society BKMS

In this paper, we give some results on 2-strongly Gorenstein projective modules and related rings. We first investigate the relationship between strongly Gorenstein projective modules and periodic modules and then give the structure of modules over strongly Gorenstein semisimple rings. Furthermore, we prove that a ring $R$ is 2-strongly Gorenstein hereditary if and only if every ideal of $R$ is Gorenstein projective and the class of 2-strongly Gorenstein projective modules is closed under extensions. Finally, we study the relationship between 2-Gorenstein projective hereditary and 2-Gorenstein projective semisimple rings, and we also give an example to show the quotient ring of a 2-Gorenstein projective hereditary ring is not necessarily 2-Gorenstein projective semisimple.

Keywords: 2-strongly Gorenstein projective, Gorenstein semisimple rings, 2-strongly Gorenstein hereditary

MSC numbers: Primary 13C10, 16E65, 18G20, 18G25, 18G35

Supported by: This work was financially supported by NSFC(11671283) and NSFC(11401493).