Divisibility and groups in one-generated semirings

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F18%3A00322037" target="_blank" >RIV/68407700:21230/18:00322037 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1142/S0219498818500718" target="_blank" >http://dx.doi.org/10.1142/S0219498818500718</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0219498818500718" target="_blank" >10.1142/S0219498818500718</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Divisibility and groups in one-generated semirings

Popis výsledku v původním jazyce

Let (S,+, .) be a semiring generated by one element. Let us denote this element by w is an element of S and let g(x) is an element of x . N[x] be a polynomial. It has been proved that if g(x) contains at least two different monomials, then the elements of the form g(w) may possibly be contained in any countable commutative semigroup. In particular, divisibility of such elements does not imply their torsion. Let, on the other hand, g(x) consist of a single monomial (i.e. g(x) = kx(n), where k, n is an element of N). We show that in this case, the divisibility of g(w) by infinitely many primes implies that g(w) generates a group within (S, +). Further, an element a is an element of S is called an m-fraction of an element z is an element of S if m is an element of N and z = m . a. We prove that "almost every" m-fraction of w(n) can be expressed as f(w) for some polynomial f is an element of x . N[x] of degree at most n.

Název v anglickém jazyce

Divisibility and groups in one-generated semirings

Popis výsledku anglicky

Let (S,+, .) be a semiring generated by one element. Let us denote this element by w is an element of S and let g(x) is an element of x . N[x] be a polynomial. It has been proved that if g(x) contains at least two different monomials, then the elements of the form g(w) may possibly be contained in any countable commutative semigroup. In particular, divisibility of such elements does not imply their torsion. Let, on the other hand, g(x) consist of a single monomial (i.e. g(x) = kx(n), where k, n is an element of N). We show that in this case, the divisibility of g(w) by infinitely many primes implies that g(w) generates a group within (S, +). Further, an element a is an element of S is called an m-fraction of an element z is an element of S if m is an element of N and z = m . a. We prove that "almost every" m-fraction of w(n) can be expressed as f(w) for some polynomial f is an element of x . N[x] of degree at most n.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Journal of Algebra and Its Applications (JAA)

ISSN

0219-4988

e-ISSN

1793-6829

Svazek periodika

17

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

10

Strana od-do

1-10

Kód UT WoS článku

000429156500013

EID výsledku v databázi Scopus

2-s2.0-85019021789