Vol. 65, No. 1, 1976

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Faithful distributive modules over incidence algebras

Robert Benjamin Feinberg

Vol. 65 (1976), No. 1, 35–45

Let Q be a lower finite quasi-ordered set and let I(Q) be the incidence algebra of Q over a field K. In this paper we determine all faithful distributive modules over I(Q) and relate the result to the structure of the outer automorphism group of the algebra. In the case when Q is finite we also determine all left ideals L of I(Q) such that I(Q)I(Q)∕L is a faithful distributive module over I(Q).

Mathematical Subject Classification
Primary: 16A64, 16A64
Secondary: 06A70
Received: 20 November 1975
Published: 1 July 1976
Robert Benjamin Feinberg