Additively idempotent matrix semirings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00389452" target="_blank" >RIV/68407700:21230/25:00389452 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1142/S0219498825500136" target="_blank" >https://doi.org/10.1142/S0219498825500136</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0219498825500136" target="_blank" >10.1142/S0219498825500136</a>

Result language
angličtina
Original language name
Additively idempotent matrix semirings
Original language description
Let S be an additively idempotent semiring and M-n(S) be the semiring of all nxn matrices over S. We characterize the conditions of when the semiring M-n(S) is congruence-simple provided that the semiring S is either commutative or finite. We also give a characterization of when the semiring M-n(S) is subdirectly irreducible for S being almost integral (i.e. xy + yx + x = x for all x, y is an element of S). In particular, we provide this characterization for the semirings S derived from the pseudo MV-algebras.
Czech name
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Czech description
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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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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