Generation of summand absorbing submodules

Zur Izhakian, Manfred Knebusch, Louis Rowen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 â'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.

Original languageEnglish
Article number2150201-1
JournalJournal of Algebra and its Applications
Early online date20 Aug 2020
Publication statusE-pub ahead of print - 20 Aug 2020


  • additive spine
  • direct sum decomposition
  • free (semi)module
  • halo
  • lacking zero sums
  • matrices
  • Semigroup
  • semiring
  • summand absorbing submodule
  • tropical space


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