Abstract
We study to classify, up to isomorphism, algebras Λ over a field k such that the radical cubed is zero and Λ modulo the radical is a product of copies of k. The number of local quasi-Frobenius k-algebras with the condition is shown to be not less than the cardinality of k. In particular, the canonical forms of those algebras of dimension 5 are presented and their isomorphism classes are completely determined under some conditions on k.
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Kikumasa, I., Oshiro, K. & Yoshimura, H. Isomorphism Classes of Algebras with Radical Cube Zero II. Appl Categor Struct 16, 297–310 (2008). https://doi.org/10.1007/s10485-007-9103-6
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DOI: https://doi.org/10.1007/s10485-007-9103-6