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Torsion and divisibility in finitely generated commutative semirings

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00315608" target="_blank" >RIV/68407700:21230/17:00315608 - isvavai.cz</a>

  • Alternative codes found

    RIV/00216224:14310/17:00108050

  • Result on the web

    <a href="http://dx.doi.org/10.1007/s00233-016-9827-4" target="_blank" >http://dx.doi.org/10.1007/s00233-016-9827-4</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>

Alternative languages

  • 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

Classification

  • 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

Result continuities

  • Project

    <a href="/en/project/GP13-29835P" target="_blank" >GP13-29835P: Structure of commutative semirings</a><br>

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2017

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Semigroup Forum

  • ISSN

    0037-1912

  • e-ISSN

    1432-2137

  • Volume of the periodical

    95

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    10

  • Pages from-to

    293-302

  • UT code for WoS article

    000413680900004

  • EID of the result in the Scopus database

    2-s2.0-84990831269