Abstract
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 language | English |
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Article number | 2150201 |
Number of pages | 26 |
Journal | Journal of Algebra and its Applications |
Volume | 20 |
Issue number | 11 |
Early online date | 20 Aug 2020 |
DOIs | |
Publication status | Published - 2021 |
Keywords
- additive spine
- direct sum decomposition
- free (semi)module
- halo
- lacking zero sums
- matrices
- Semigroup
- semiring
- summand absorbing submodule
- tropical space