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Homology of systemic modules
manuscripta mathematica ( IF 0.6 ) Pub Date : 2021-02-09 , DOI: 10.1007/s00229-021-01272-z
Jaiung Jun , Kalina Mincheva , Louis Rowen

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.



中文翻译:

系统模块的同源性

在本文中,我们发展了热带同源理论的基础。我们使用“三元组”和“系统”的语言同时处理来自各种方法的热带数学结构,包括半环,超场和超热带代数。我们用否定图丰富了代数结构,而否定图则自然而然。我们获得了Schanuel引理的一个类似物,该引理使我们可以讨论这种情况下模块的投影维。我们定义了同源性和准确性的两个不同版本,并研究了它们的属性。我们还证明了弱的Snake引理类型结果。

更新日期:2021-02-10
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