{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:38:08Z","timestamp":1776728288101,"version":"3.51.2"},"reference-count":17,"publisher":"American Mathematical Society (AMS)","issue":"238","license":[{"start":{"date-parts":[[2002,12,21]],"date-time":"2002-12-21T00:00:00Z","timestamp":1040428800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The Auslander-Reiten quiver of a finite-dimensional associative algebra\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A\">\n                        <mml:semantics>\n                          <mml:mi>A<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">A<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    encodes information about the indecomposable finite-dimensional representations of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A\">\n                        <mml:semantics>\n                          <mml:mi>A<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">A<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and their homomorphisms. A component of the Auslander-Reiten quiver is called preprojective if it does not admit oriented cycles and each of its modules can be shifted into a projective module using the Auslander-Reiten translation. Preprojective components play an important role in the present research on algebras of finite and tame representation type. We present an algorithm which detects all preprojective components of a given algebra.\n                  <\/p>","DOI":"10.1090\/s0025-5718-01-01404-1","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"743-759","source":"Crossref","is-referenced-by-count":1,"title":["An algorithm for finding all preprojective components of the Auslander-Reiten quiver"],"prefix":"10.1090","volume":"71","author":[{"given":"Peter","family":"Dr\u00e4xler","sequence":"first","affiliation":[]},{"given":"Klara","family":"K\u00f6gerler","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,12,21]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1080\/00927877508822046","article-title":"Representation theory of Artin algebras. III. Almost split sequences","volume":"3","author":"Auslander, Maurice","year":"1975","journal-title":"Comm. 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