2015/10/16 by Denise A. Rangel Tracy, Tracy, Denise A. Rangel
Mathematics · #13D99: 18G99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1510.04922
openalex publication_date 2015/10/16 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We consider local non-Gorenstein rings of the form (Si,\mathfrakni)=k[X, Y1, … ,Yi]/(X2, (Y1, …, Yi)2), where i≥ 2. We show that every totally reflexive Si-module has a presentation matrix of the form I x + ∑j=1i Bj yj, where I is the identity matrix and Bj 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 Si which are minimal generated by n elements and the set of i-tuples of n × n matrices with entries in k modulo a certain equivalence relation.