Proceedings of the American Mathematical Society

Author(s): Yongzhi Cao
Journal: Proc. Amer. Math. Soc. 132 (2004), 1613-1619.
MSC (2000): Primary 16G30; Secondary 18G05
Posted: November 25, 2003
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Abstract: We show that the projective module

over a cellular algebra is injective if and only if the socle of

coincides with the top of

, and this is also equivalent to the condition that the

th socle layer of

is isomorphic to the

th radical layer of

for each positive integer

. This eases the process of determining the Loewy series of the projective-injective modules over cellular algebras.

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