Auslander Class, G_C, and C–projective Modules Modulo Exact Zero-divisors

Abstract

For a semidualizing module C over a ring R, we study the following classes modulo exact zero divisors: G _C –projectives, 𝒢 _C ; the Auslander class 𝒜 _C ; the Bass class ℬ _C ; 𝒫 _C –projective; ℱ _C –projective; and ℐ _C –injective dimensions.

Key Words:

• Auslander class
• Bass class
• C–flat
• C–injective
• C–projective
• Exact zero–divisor
• G _C –projective
• Semidualizing

2010 Mathematics Subject Classification:

• 13D02
• 13D05
• 13D07

ACKNOWLEDGMENT

The authors thanks Sean Sather-Wagsaff for reading the manuscript and his communications. They are also grateful to the referee for her/his invaluable comments.

Notes

Communicated by S. Goto.