A description of totally reflexive modules for a class of non-Gorenstein rings
DAR Tracy - arXiv preprint arXiv:1510.04922, 2015 - arxiv.org
We consider local non-Gorenstein rings of the form $(S_i,\mathfrak {n} _i)= k [X, Y_1,\ldots,
Y_i]/\left (X^ 2,(Y_1,\ldots, Y_i)^ 2\right), $ where $ i\geq 2. $ We show that every totally
reflexive $ S_i $-module has a presentation matrix of the form $ I x+\sum_ {j= 1}^ i B_j y_j, $
where $ I $ is the identity matrix and $ B_j $ is an square matrix with entries in the residue
field, $ k $. From there, we prove that there exists a bijection between the set of isomorphism
classes of totally reflexive modules (without projective summands) over $ S_i $ which are …
Y_i]/\left (X^ 2,(Y_1,\ldots, Y_i)^ 2\right), $ where $ i\geq 2. $ We show that every totally
reflexive $ S_i $-module has a presentation matrix of the form $ I x+\sum_ {j= 1}^ i B_j y_j, $
where $ I $ is the identity matrix and $ B_j $ is an square matrix with entries in the residue
field, $ k $. From there, we prove that there exists a bijection between the set of isomorphism
classes of totally reflexive modules (without projective summands) over $ S_i $ which are …
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