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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the projective-injective modules over cellular algebras


Author: Yongzhi Cao
Journal: Proc. Amer. Math. Soc. 132 (2004), 1613-1619
MSC (2000): Primary 16G30; Secondary 18G05
Published electronically: November 25, 2003
MathSciNet review: 2051121
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Abstract: We show that the projective module $P$ over a cellular algebra is injective if and only if the socle of $P$ coincides with the top of $P$, and this is also equivalent to the condition that the $m$th socle layer of $P$ is isomorphic to the $m$th radical layer of $P$ for each positive integer $m$. This eases the process of determining the Loewy series of the projective-injective modules over cellular algebras.


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Additional Information

Yongzhi Cao
Affiliation: Department of Mathematics, Beijing Normal University, 100875 Beijing, People’s Republic of China
Address at time of publication: State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, People’s Republic of China
Email: yongzhic@263.net

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07268-X
PII: S 0002-9939(03)07268-X
Received by editor(s): November 11, 2002
Received by editor(s) in revised form: February 23, 2003
Published electronically: November 25, 2003
Communicated by: Martin Lorenz
Article copyright: © Copyright 2003 American Mathematical Society