Název: Semigroup Structure of Sets of Solutions to Equation X^s = X^m
Autoři: Porubský, Štefan
Typ dokumentu: Výzkumné zprávy
Rok: 2017
Jazyk: eng
Edice: Technical Report, svazek: V-1247
Abstrakt: Using an idempotent semigroup approach we describe the semigroup and group structure of the set of solutions to equation X^m = X^s in successive steps over a periodic commutative semigroup, over multiplicative semigroups of factor rings of residually finite commutative rings and finally over multiplicative semigroups of factor rings of residually finite commutative principal ideal domains. The analysis is done through the use of the maximal subsemigroups and groups corresponding to an idempotent of the corresponding semigroup and in the case of residually finite PID’s employing the available analysis of the Euler-Fermat Theorem as given in [11]. 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 connected with the message space of RSA cryptosystems and Fermat pseudoprimes.
Klíčová slova: equation X^s = X^m; finite commutative ring with identity element; idempotent; maximal group corresponding to an idempotent; maximal semigroup corresponding to an idempotent; residually finite commutative principal ideal domains; set of solutions
Číslo projektu: GA17-02804S (CEP)
Poskytovatel projektu: GA ČR

Instituce: Ústav informatiky AV ČR (web)
Informace o dostupnosti dokumentu: Dokument je dostupný na vyžádání prostřednictvím repozitáře Akademie věd.
Původní záznam: http://hdl.handle.net/11104/0273446

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-361692


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