Projective systemic modules

Jaiung Jun, Kalina Mincheva, Louis Rowen

    Research output: Contribution to journalArticlepeer-review

    4 Scopus citations


    We develop the basic theory of projective modules and splitting over semirings, within the more general setting of systems. Systems provide a common language for most tropical algebraic approaches including supertropical algebra, hyperrings (specifically hyperfields), and fuzzy rings. This enables us to prove analogues of classical theorems for tropical and hyperring theory in a unified way. In this context we prove a Dual Basis Lemma and versions of Schanuel's Lemma.

    Original languageEnglish
    Article number106243
    JournalJournal of Pure and Applied Algebra
    Issue number5
    StatePublished - May 2020

    Bibliographical note

    Funding Information:
    Acknowledgments J.J. was supported by AMS-Simons travel grant. K.M. was supported by the Institute Mittag-Leffler and the “Vergstiftelsen”. K.M. would like to thank the Institute Mittag-Leffler for its hospitality. Part of this work has been carried out during the workshop “Workshop on Tropical varieties and amoebas in higher dimension” in which K.M. and L.R. participated.

    Publisher Copyright:
    © 2019 Elsevier B.V.


    • Module
    • Projective
    • Schanuel's Lemma
    • Supertropical algebra
    • Symmetrization
    • System


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