Let be a commutative Noetherian ring and let be an ideal of . In this paper, after recalling briefly the main properties of the amalgamated duplication ring which is introduced by D'Anna and Fontana, we restrict our attention to the study of the properties of , when is a semidualizing ideal of , i.e., is an ideal of and is a semidualizing -module. In particular, it is shown that if is a semidualizing ideal and is a finitely generated -module, then is totally -reflexive as an -module if and only if is totally reflexive as an -module. In addition, it is shown that if is a semidualizing ideal, then and are Gorenstein projective over , and every injective -module is Gorenstein injective as an -module. Finally, it is proved that if is a non-zero flat ideal of , then fd , for every -module .
Cite this article
Maryam Salimi, Elham Tavasoli, S. Yassemi, The Amalgamated Duplication of a Ring Along a Semidualizing Ideal. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 115–127