Izhakian, Zur and Knebusch, Manfred and Rowen, Louis (2019) Summand absorbing submodules of a module over a semiring. JOURNAL OF PURE AND APPLIED ALGEBRA, 223 (8). pp. 3262-3294. ISSN 0022-4049, 1873-1376
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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, we call a submodule W of V "summand absorbing" (SA) in V 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 arise in tropical algebra and modules over idempotent semirings, as well as modules over semirings of sums of squares. We explore the lattice of finite sums of SA-submodules, obtaining analogs of the Jordan-Holder theorem, the noetherian theory, and the lattice-theoretic Krull dimension. We pay special attention to finitely generated SA-submodules, and describe their explicit generation. (C) 2018 Elsevier B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Semiring; Lacking zero sums; Direct sum decomposition; Projective (semi)module; Indecomposable; Upper bound monoid |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Manfred Knebusch |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Apr 2020 06:54 |
| Last Modified: | 07 Apr 2020 06:54 |
| URI: | https://pred.uni-regensburg.de/id/eprint/26588 |
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