Projective systemic modules

Jaiung Jun; Kalina Mincheva; Louis Rowen

doi:10.1016/j.jpaa.2019.106243

Projective systemic modules

Jaiung Jun, Kalina Mincheva, Louis Rowen

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 language	English
Article number	106243
Journal	Journal of Pure and Applied Algebra
Volume	224
Issue number	5
DOIs	https://doi.org/10.1016/j.jpaa.2019.106243
State	Published - 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.

Keywords

Module
Projective
Schanuel's Lemma
Supertropical algebra
Symmetrization
System

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10.1016/j.jpaa.2019.106243

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Projective systemic modules

Abstract

Bibliographical note

Keywords

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