Characterizations of regular local rings via syzygy modules of the residue field

Dipankar Ghosh, Anjan Gupta, Tony J. Puthenpurakal

Let $R$ be a commutative Noetherian local ring with residue field $k$. We show that if a finite direct sum of syzygy modules of $k$ surjects onto `a semidualizing module' or `a non…