Torsion and divisibility in finitely generated commutative semirings

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21230/17:00315608

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Torsion and divisibility in finitely generated commutative semirings

Popis výsledku v původním jazyce

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)).

Název v anglickém jazyce

Torsion and divisibility in finitely generated commutative semirings

Popis výsledku anglicky

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)).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GP13-29835P" target="_blank" >GP13-29835P: Struktura komutativních polookruhů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Semigroup Forum

ISSN

0037-1912

e-ISSN

1432-2137

Svazek periodika

95

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

293-302

Kód UT WoS článku

000413680900004

EID výsledku v databázi Scopus

2-s2.0-84990831269