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 Ext^1_R((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.