New results related to a conjecture of Moore

作者：Bahlekeh A^*; Salarian Sh

来源：ARCHIV DER MATHEMATIK, 2013, 100(3): 231-239.

DOI：10.1007/s00013-013-0490-7

• Gorenstein projective
• Moore's conjecture
• Injectivity over group rings
• Kropholler's hierarchy
• LHF

Let I" be a group, I"' be a subgroup of I" of finite index, and R be a ring with identity. Assume that M is an RI"-module whose restriction to RI"' is projective. Moore's conjecture: Assume that, for all , either there is an integer n such that or x has finite order and is invertible in R. Then M is also projective over RI". In this paper, we consider an analogue of this conjecture for injective modules. It turns out that the validity of the conjecture for injective modules implies the validity of it on projective and flat modules. It is also shown that the conjecture for injective modules is true whenever I" belongs to Kropholler's hierarchy . In addition, assume that M is an RI"-module whose restriction to RI"' is Gorenstein projective (resp. injective), it is proved that M is Gorenstein projective (resp. injective) over RI" whenever I"' is a subgroup of I" of finite index.

• 出版日期2013-3