Semigroup Structure of Sets of Solutions to Equation X^m = X^s

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F18%3A00493285" target="_blank" >RIV/67985807:_____/18:00493285 - isvavai.cz</a>

Výsledek na webu

<a href="http://ac.inf.elte.hu/Vol_048_2018/151_48.pdf" target="_blank" >http://ac.inf.elte.hu/Vol_048_2018/151_48.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Semigroup Structure of Sets of Solutions to Equation X^m = X^s

Popis výsledku v původním jazyce

We describe the semigroup and group structure of the set of solutions to equation X^m = X^s over the multiplicative semigroups of factor rings of residually finite commutative rings and of residually finite commutative PID’s. The analysis is done in terms of the structure of maximal unipotent subsemigroups and subgroups of semigroups of the corresponding rings. In case of residually finite PID’s we employ the available idempotents analysis of the Euler–Fermat Theorem in these rings used to determine minimal positive integers nu and nu such that for all elements x of these rings one has x^(kappa+delta)= x^kappa. In particular, the case when this set of solutions is a union of groups is handled. As a simple application we show a not yet noticed group structure of the set of solutions to x^n = x (mod n) connected with the message space of RSA cryptosystems and Fermat pseudoprimes.

Název v anglickém jazyce

Semigroup Structure of Sets of Solutions to Equation X^m = X^s

Popis výsledku anglicky

We describe the semigroup and group structure of the set of solutions to equation X^m = X^s over the multiplicative semigroups of factor rings of residually finite commutative rings and of residually finite commutative PID’s. The analysis is done in terms of the structure of maximal unipotent subsemigroups and subgroups of semigroups of the corresponding rings. In case of residually finite PID’s we employ the available idempotents analysis of the Euler–Fermat Theorem in these rings used to determine minimal positive integers nu and nu such that for all elements x of these rings one has x^(kappa+delta)= x^kappa. In particular, the case when this set of solutions is a union of groups is handled. As a simple application we show a not yet noticed group structure of the set of solutions to x^n = x (mod n) connected with the message space of RSA cryptosystems and Fermat pseudoprimes.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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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

Universitatis Scientiarum Budapestinensis de Rolando Eotvos Nominatae. Annales. Sectio Computatorica

ISSN

0138-9491

e-ISSN

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Svazek periodika

48

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

17

Strana od-do

151-167

Kód UT WoS článku

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EID výsledku v databázi Scopus

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