Torsion factors of commutative monoid semirings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00373291" target="_blank" >RIV/68407700:21230/23:00373291 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00233-023-10350-5" target="_blank" >https://doi.org/10.1007/s00233-023-10350-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00233-023-10350-5" target="_blank" >10.1007/s00233-023-10350-5</a>

Result language
angličtina
Original language name
Torsion factors of commutative monoid semirings
Original language description
Let P be a finitely generated commutative semiring with a unity. It was shown recently that if the multiplicative reduct of P is a group then P is additively idempotent. We extend this result by showing that P is additively idempotent, provided that P is additively divisible. We further generalize this result using a weaker form of divisibility (almost-divisibility) as follows. Let S be a semiring that is a factor of a monoid semiring N[C] where C is a submonoid of a free commutative monoid of finite rank. Then the semiring S is additively almost-divisible if and only if S is torsion. In particular, we show that if S is a ring then S contains no non-finitely generated subring of Q.
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
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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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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