On the projective-injective modules over cellular algebras

Cao, Yongzhi

doi:10.1090/S0002-9939-03-07268-X

On the projective-injective modules over cellular algebras
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Proc. Amer. Math. Soc. 132 (2004), 1613-1619 Request permission

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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