Dense Ideals and Maximal Quotient Rings of Incidence Algebras

In this paper, we determine a core subset of dense ideals and left dense ideals of some incidence algebras. As an application and the motivation of this work, we compute the maximal left quotient ring of some incidence algebras. In a ring T, if a minimal left dense ideal, D exists, then the maximal...

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Bibliographic Details
Published in:Communications in algebra 2003-01, Vol.31 (11), p.5287-5304
Main Author: Kanuni, Müge
Format: Article
Language:English
Subjects:
Dense ideals
Incidence algebras
Quotient rings
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Summary:In this paper, we determine a core subset of dense ideals and left dense ideals of some incidence algebras. As an application and the motivation of this work, we compute the maximal left quotient ring of some incidence algebras. In a ring T, if a minimal left dense ideal, D exists, then the maximal left quotient ring of T is isomorphic to the ring of T-module homomorphisms of D into D (Lambek, J. (1963). On Utumi's ring of quotients. Can. J. Math. 15:363-370). Hence, in the case of an incidence algebra, we give necessary and sufficient conditions for a minimal left dense ideal to exist and give a description of this ideal when it exists.
ISSN:0092-7872
1532-4125
DOI:10.1081/AGB-120023955