Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Classification of modules for infinite-dimensional string algebras
HTML articles powered by AMS MathViewer

by William Crawley-Boevey PDF
Trans. Amer. Math. Soc. 370 (2018), 3289-3313 Request permission


We relax the definition of a string algebra to also include infinite-dimensional algebras such as $k[x,y]/(xy)$. Using the functorial filtration method, which goes back to Gelfand and Ponomarev, we show that finitely generated modules and artinian modules (and more generally finitely controlled and pointwise artinian modules) are classified in terms of string and band modules. This subsumes the known classifications of finite-dimensional modules for string algebras and of finitely generated modules for $k[x,y]/(xy)$. Unlike in the finite-dimensional case, the words parameterizing string modules may be infinite.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 16D70, 13C05
  • Retrieve articles in all journals with MSC (2010): 16D70, 13C05
Additional Information
  • William Crawley-Boevey
  • Affiliation: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
  • Address at time of publication: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
  • MR Author ID: 230720
  • Email:
  • Received by editor(s): March 7, 2016
  • Received by editor(s) in revised form: July 26, 2016
  • Published electronically: December 20, 2017
  • Additional Notes: This material is based upon work supported by the National Science Foundation under grant No. 0932078 000 while the author was in residence at the Mathematical Science Research Institute (MSRI) in Berkeley, California, during the spring semester 2013.
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 3289-3313
  • MSC (2010): Primary 16D70; Secondary 13C05
  • DOI:
  • MathSciNet review: 3766850