Homology of systemic modules

Jaiung Jun; Kalina Mincheva; Louis Rowen

doi:10.1007/s00229-021-01272-z

Homology of systemic modules

Jaiung Jun, Kalina Mincheva, Louis Rowen

Department of Mathematics

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

2 Scopus citations

Abstract

In this paper, we develop the rudiments of a tropical homology theory. We use the language of “triples” and “systems” to simultaneously treat structures from various approaches to tropical mathematics, including semirings, hyperfields, and super tropical algebra. We enrich the algebraic structures with a negation map where it does not exist naturally. We obtain an analogue to Schanuel’s lemma which allows us to talk about projective dimension of modules in this setting. We define two different versions of homology and exactness, and study their properties. We also prove a weak Snake lemma type result.

Original language	English
Pages (from-to)	469-520
Number of pages	52
Journal	Manuscripta Mathematica
Volume	167
Issue number	3-4
DOIs	https://doi.org/10.1007/s00229-021-01272-z
State	Published - Mar 2022

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.

Funding

J.J. was supported by an AMS-Simons travel grant.

Funders	Funder number
AMS-Simons

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10.1007/s00229-021-01272-z

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Homology of systemic modules

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