Izhakian, Zur and Knebusch, Manfred and Rowen, Louis (2021) Generation of summand absorbing submodules. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 20 (11): 2150201. ISSN 0219-4988, 1793-6829
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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 is an element of V, x + y is an element of W double right arrow x is an element of W,y is an element of 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Semigroup; semiring; lacking zero sums; direct sum decomposition; free (semi)module; summand absorbing submodule; halo; additive spine; matrices; tropical space |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Manfred Knebusch |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 01 Sep 2022 05:49 |
| Last Modified: | 01 Sep 2022 05:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/47129 |
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