Torsion and divisibility in finitely generated commutative semirings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F17%3A00108050" target="_blank" >RIV/00216224:14310/17:00108050 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21230/17:00315608
Result on the web
<a href="https://link.springer.com/content/pdf/10.1007/s00233-016-9827-4.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007/s00233-016-9827-4.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00233-016-9827-4" target="_blank" >10.1007/s00233-016-9827-4</a>

Result language
angličtina
Original language name
Torsion and divisibility in finitely generated commutative semirings
Original language description
It is conjectured that (additive) divisibility is equivalent to (additive) idempotency in a finitely generated commutative semiring S. In this paper we extend this conjecture to weaker forms of these properties-torsion and almost-divisibility (an element a is an element of S is called almost-divisible in S if there is b is an element of Nsuch that b is divisible in S by infinitely many primes). We show that a one-generated semiring is almost-divisible if and only if it is torsion. In the case of a free commutative semiring F(X) we characterize those elements f is an element of F(X) such that for every epimorphism pi of F(X) torsion and almost-divisibility of pi(f) are equivalent in pi (F(X)).
Czech name
—
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
<a href="/en/project/GP13-29835P" target="_blank" >GP13-29835P: Structure of commutative semirings</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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