A Construction of Totally Reflexive Modules |
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| Authors: | Hamid Rahmati Janet Striuli Roger Wiegand |
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| Institution: | 1.Department of Mathematics Miami University,Oxford,USA;2.Department of Mathematics Fairfield University,Fairfield,USA;3.Department of Mathematics University of Nebraska,Lincoln,USA |
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| Abstract: | 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. |
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