Semimodules over commutative semirings and modules over unitary commutative rings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73612774" target="_blank" >RIV/61989592:15310/22:73612774 - isvavai.cz</a>
Result on the web
<a href="https://www.tandfonline.com/doi/epdf/10.1080/03081087.2020.1760192" target="_blank" >https://www.tandfonline.com/doi/epdf/10.1080/03081087.2020.1760192</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/03081087.2020.1760192" target="_blank" >10.1080/03081087.2020.1760192</a>

Result language
angličtina
Original language name
Semimodules over commutative semirings and modules over unitary commutative rings
Original language description
It is known that the lattice of submodules of a module is modular. However, this is not the case for the lattice of subsemimodules of a semimodule. We show examples and describe these lattices for a given semimodule. We study closed and splitting subsemimodules and submodules of a given semimodule or module M, respectively. We derive a sufficient condition under which the lattice Lc(M) of closed subsemimodules is a homomorphic image of the lattice L(M) of all subsemimodules. We describe the ordered set of splitting submodules of a module and show a natural bijective correspondence between this poset and the poset of all projections of this module. We show that this poset is orthomodular. This result extendes the case known for posets of closed subspaces of a Hilbert space which is used in the logic of quantum mechanics.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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