FP-INJECTIVE SEMIRINGS, SEMIGROUP RINGS AND LEAVITT PATH ALGEBRAS

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    Abstract

    In this paper we give characterisations of FP-injective semirings (previously termed “exact” semirings in work of the first author). We provide a basic connection between FP-injective semirings and P-injective semirings, and establish that FP-injectivity of semirings is a Morita invariant property. We show that the analogue of the Faith-Menal conjecture (relating FP-injectivity and self-injectivity for rings satisfying certain chain conditions) does not hold for semirings. We prove that the semigroup ring of a locally finite inverse monoid over an FP-injective ring is FP-injective and give a criterion for the Leavitt path algebra of a finite graph to be FP-injective.
    Original languageEnglish
    Pages (from-to)1893-1906
    Number of pages14
    JournalCommunications in Algebra
    Volume45
    Issue number5
    Early online date7 Oct 2016
    DOIs
    Publication statusPublished - 2017

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