FP-INJECTIVE SEMIRINGS, SEMIGROUP RINGS AND LEAVITT PATH ALGEBRAS

Research output: Contribution to journalArticle

  • Authors:
  • Marianne Johnson
  • T.G. Nam

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.

Bibliographical metadata

Original languageEnglish
Pages (from-to)1893-1906
Number of pages14
JournalCommunications in Algebra
Volume45
Issue number5
Early online date7 Oct 2016
DOIs
StatePublished - 2017