Projective systemic modules

被引：6
|
作者：
Jun, Jaiung [1 ]
Mincheva, Kalina [2 ]
Rowen, Louis [3 ]
机构：
[1] SUNY Coll New Paltz, Dept Math, New Paltz, NY 12561 USA
[2] Yale Univ, Dept Math, New Haven, CT 06511 USA
[3] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel
来源：
JOURNAL OF PURE AND APPLIED ALGEBRA | 2020年 / 224卷 / 05期
关键词：
Projective; System; Symmetrization; Supertropical algebra; Module; Schanuel's Lemma; HOMOLOGICAL CHARACTERIZATION;
D O I：
10.1016/j.jpaa.2019.106243
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2019 Elsevier B.V. All rights reserved.
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页数：27
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