The Auslander–Reiten Components in the Rhombic Picture

REFERENCES

• Assem , I. , Simson , D. , Skowroński , A. ( 2006 ). Elements of the Representation Theory of Associative Algebras 1: Techniques of Representation Theory . Cambridge : Cambridge Univ. Press .
   Google Scholar
• Auslander , M. , Reiten , I. , Smalø , S. ( 1995 ). Representation Theory of Artin Algebras . Cambridge : Cambridge Univ. Press .
   Google Scholar
• Butler , M. C. R. , Ringel , C. M. ( 1987 ). Auslander–Reiten sequences with few middle terms and applications to string algebras . Comm. Algebra 15 : 145 – 179 .
   Web of Science ®Google Scholar
• Chen , B. ( 2008 ). The Gabriel-Roiter Measure for . J. Algebra 320 : 2891 – 2906 .
   Web of Science ®Google Scholar
• Chen , B. ( 2008 ). Comparison of Auslander-Reiten theory and Gabriel-Roiter measure approach to the module categories of tame hereditary algebras . Comm. Algebra 36 : 4186 – 4200 .
   Web of Science ®Google Scholar
• Dung , N. V. , Simson , D. ( 2008 ). The Gabriel-Roiter measure for right pure semisimple rings . Algebr. Represent. Theory 11 : 407 – 424 .
   Web of Science ®Google Scholar
• Krause , H. ( 1991 ). Maps between tree and band modules . J. Algebra 137 : 186 – 194 .
   Web of Science ®Google Scholar
• Ringel , C. M. ( 1984 ). Tame Algebras and Integral Quadratic Forms . Vol. 1099 Lecture Notes in Math. Springer-Verlag .
   Google Scholar
• Ringel , C. M. ( 2005 ). The Gabriel-Roiter measure . Bull. Sci. Math. 129 : 726 – 748 .
   Web of Science ®Google Scholar
• Ringel , C. M. ( 2010 ). Gabriel-Roiter inclusions and Auslander–Reiten theory . J. Algebra 324 : 3579 – 3590 .
   Web of Science ®Google Scholar
• Communicated by D. Zacharia.
   Google Scholar