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On incidence modulo ideal rings. (English) Zbl 1162.16010

The authors introduce a class of rings which can be regarded as liftings of incidence algebras of a finite poset to Krull dimension 1. More precisely, such “incidence modulo ideal rings” are related to incidence algebras like connected basic hereditary orders to triangular matrix rings. Some relationships to semiperfect rings and their quivers, and applications to the general linear group are given.

MSC:

16P40 Noetherian rings and modules (associative rings and algebras)
16S99 Associative rings and algebras arising under various constructions
16G20 Representations of quivers and partially ordered sets
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