FP-injective semirings,semigroup rings and Leavitt path algebras |
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Authors: | Marianne Johnson Tran Giang Nam |
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Institution: | 1. School of Mathematics, University of Manchester, Manchester, UKMarianne.Johnson@maths.manchester.ac.uk tgnam@math.ac.vn;3. Institute of Mathematics, VAST, Cau Giay, Hanoi, Vietnam |
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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. |
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Keywords: | Exact semiring FP-injective semiring Leavitt path algebra |
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