Title: Classification of finitely generated modules for k[x,y]/(xy) and generalizations
Abstract: We relax the definition by Butler and Ringel of a 'string algebra' to also include infinite-dimensional algebras such as k[x,y]/(xy). We show that finitely generated modules (and more generally what we call 'finitely controlled' modules for such algebras are direct sums of string and band modules. This subsumes the known classifications of finite-dimensional modules for string algebras and of finitely generated modules for k[x,y]/(xy). The string and band modules are parameterized by certain 'words' which, unlike in the finite-dimensional case, may be infinite. We show that the Krull-Remak-Schmidt property holds.
Publication Year: 2013
Publication Date: 2013-08-29
Language: en
Type: preprint
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Cited By Count: 2
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