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

Result code in 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>
Result on the web
<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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Result language
angličtina
Original language name
Semigroup Structure of Sets of Solutions to Equation X^m = X^s
Original language description
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.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical
Universitatis Scientiarum Budapestinensis de Rolando Eotvos Nominatae. Annales. Sectio Computatorica
ISSN
0138-9491
e-ISSN
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Volume of the periodical
48
Issue of the periodical within the volume
1
Country of publishing house
HU - HUNGARY
Number of pages
17
Pages from-to
151-167
UT code for WoS article
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EID of the result in the Scopus database
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