A Construction of Totally Reflexive Modules
We construct infinite families of pairwise non-isomorphic indecomposable totally reflexive modules of high multiplicity. Under suitable conditions on the totally reflexive modules M and N, we find infinitely many non-isomorphic indecomposable modules arising as extensions of M by N. The construction uses the bimodule structure of Ext1R((M,N) over the endomorphism rings of N and M. Our results compare with a recent theorem of Celikbas, Gheibi and Takahashi, and broaden the scope of that theorem.
Algebras and Representation Theory
Hamid, Rahmati; Striuli, Janet; and Wiegand, Roger, "A Construction of Totally Reflexive Modules" (2016). Mathematics Faculty Publications. 54.
Rahmati, Hamid, Janet Striuli, and Roger Wiegand. "A Construction of Totally Reflexive Modules." Algebras and Representation Theory (2016): 1-9. doi:10.1007/s10468-015-9564-5.