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Generation of summand absorbing submodules
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-08-20 , DOI: 10.1142/s0219498821502017
Zur Izhakian 1 , Manfred Knebusch 2 , Louis Rowen 3
Affiliation  

An R-module V over a semiring R lacks zero sums (LZS) if x + y = 0 implies x = y = 0. More generally, a submodule W of V is “summand absorbing” (SA), if, for all x,y V, x + y W x W,y W. These relate to tropical algebra and modules over (additively) idempotent semirings, as well as modules over semirings of sums of squares. In previous work, we have explored the lattice of SA submodules of a given LZS module, especially, those that are finitely generated, in terms of the lattice-theoretic Krull dimension. In this paper, we consider which submodules are SA and describe their explicit generation.

中文翻译:

summand 吸收子模块的生成

一个R-模块在一个半环上R缺少零和 (LZS) 如果X + 是的 = 0暗示X = 是的 = 0. 更一般地,一个子模块W是“总和吸收”(SA),如果,对于所有X,是的 ,X + 是的 W X W,是的 W.这些涉及热带代数和(加法)幂等半环上的模,以及平方和半环上的模。在以前的工作中,我们已经探索了给定 LZS 模块的 SA 子模块的格,特别是根据格理论 Krull 维数有限生成的那些。在本文中,我们考虑了哪些子模块是 SA,并描述了它们的显式生成。
更新日期:2020-08-20
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