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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Quivers with relations of Harada algebras

Author(s): Kota Yamaura
Journal: Proc. Amer. Math. Soc. 138 (2010), 47-59.
MSC (2000): Primary 16G10; Secondary 16G70, 18E30
Posted: August 20, 2009
MathSciNet review: 2550169
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: For a finite dimensional algebra $ R$, we give an explicit description of quivers with relations of block extensions of $ R$. As an application, we describe quivers with relations of Harada algebras by using those of the corresponding quasi-Frobenius algebras.


References:

1.
F. W. Anderson, K. R. Fuller: Rings and Categories of Modules (second edition), Graduate Texts in Math., 13, Springer-Verlag, Heidelberg-New York-Berlin (1992). MR 1245487 (94i:16001)

2.
I. Assem, D. Simson, A. Skowroński: Elements of the Representation Theory of Associative Algebras, London Mathematical Society Student Texts, 65, Cambridge University Press (2006). MR 2197389 (2006j:16020)

3.
M. Auslander, I. Reiten: $ k$-Gorenstein algebras and syzygy modules, J. Pure Appl. Algebra 92 (1994), 1-27. MR 1259667 (95d:16008)

4.
M. Auslander, I. Reiten, S. Smalø: Representation Theory of Artin Algebras, Cambridge Studies in Advanced Mathematics, 36, Cambridge University Press (1995). MR 1314422 (96c:16015)

5.
Y. Baba, K. Iwase: On quasi-Harada rings, J. Algebra 185 (1996), 544-570. MR 1417385 (98a:16026)

6.
Y. Baba, K. Oshiro: Classical Artinian Rings and Related Topics, preprint.

7.
R. Fossum, P. Griffith, I. Reiten: Trivial Extensions of Abelian Categories, Lecture Notes in Mathematics, Vol. 456, Springer-Verlag, Berlin-New York (1975). MR 0389981 (52:10810)

8.
M. Harada: Nonsmall modules and noncosmall modules, Ring Theory. Proceedings of 1978 Antwerp Conference, Dekker, New York (1979), 669-690. MR 0563315 (81c:16022)

9.
K. Koike: Almost self-duality and Harada rings, J. Algebra 254 (2002), 336-361. MR 1933873 (2004a:16006)

10.
K. Oshiro: Lifting modules, extending modules and their applications to QF-rings, Hokkaido Math. J. 13 (1984), 310-338. MR 764267 (86b:16008a)

11.
K. Oshiro: Lifting modules, extending modules and their applications to generalized uniserial rings, Hokkaido Math. J. 13 (1984), 339-346. MR 764268 (86b:16008b)

12.
K. Oshiro: On Harada rings. I, Math. J. Okayama Univ. 31 (1989), 161-178. MR 1043359 (91f:16025)

13.
K. Oshiro: On Harada rings. II, Math. J. Okayama Univ. 31 (1989), 179-188. MR 1043359 (91f:16025)

14.
K. Oshiro: On Harada rings. III, Math. J. Okayama Univ. 32 (1990), 111-118. MR 1112019 (92k:16027)

15.
H. Tachikawa: Quasi-Frobenius rings and generalizations. $ {QF}-3$ and $ {QF}-1$ rings, Lecture Notes in Mathematics, Vol. 351, Springer-Verlag, Berlin-New York (1973). MR 0349740 (50:2233)

16.
R. M. Thrall: Some generalization of quasi-Frobenius algebras, Trans. Amer. Math. Soc. 64 (1948), 173-183. MR 0026048 (10:98c)


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Additional Information:

Kota Yamaura
Affiliation: Graduate School of Mathematics, Nagoya University, Frocho, Chikusaku, Nagoya, 464-8602, Japan
Email: m07052d@math.nagoya-u.ac.jp

DOI: 10.1090/S0002-9939-09-10006-0
PII: S 0002-9939(09)10006-0
Received by editor(s): May 21, 2008,
Received by editor(s) in revised form: April 8, 2009
Posted: August 20, 2009
Communicated by: Birge Huisgen-Zimmermann
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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