Detail publikace

Cyclicity in EL-hypergroups

NOVÁK, M. KŘEHLÍK, Š. CRISTEA, I.

Originální název

Cyclicity in EL-hypergroups

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

In the algebra of single-valued structures, cyclicity is one of the fundamental properties of groups. Therefore, it is natural to study it also in the algebra of multivalued structures (algebraic hyperstructure theory). However, when one considers the nature of generalizing this property, at least two (or rather three) approaches seem natural. Historically, all of these had been introduced and studied by 1990. However, since most of the results had originally been published in journals without proper international impact and later—without the possibility to include proper background and context-synthetized in books, the current way of treating the concept of cyclicity in the algebraic hyperstructure theory is often rather confusing. Therefore, we start our paper with a rather long introduction giving an overview and motivation of existing approaches to the cyclicity in algebraic hyperstructures. In the second part of our paper, we relate these to EL-hyperstructures, a broad class of algebraic hyperstructures constructed from (pre)ordered (semi)groups, which were defined and started to be studied much later than sources discussed in the introduction were published.

Klíčová slova

cyclic group; cyclic hypergroup; EL-hyperstructure; preorder

Autoři

NOVÁK, M.; KŘEHLÍK, Š.; CRISTEA, I.

Vydáno

7. 11. 2018

Nakladatel

MDPI

ISSN

2073-8994

Periodikum

Symmetry

Ročník

10

Číslo

11

Stát

Švýcarská konfederace

Strany od

1

Strany do

13

Strany počet

13

URL

Plný text v Digitální knihovně

BibTex

@article{BUT151055,
  author="Michal {Novák} and Štěpán {Křehlík} and Irina {Cristea}",
  title="Cyclicity in EL-hypergroups",
  journal="Symmetry",
  year="2018",
  volume="10",
  number="11",
  pages="1--13",
  doi="10.3390/sym10110611",
  issn="2073-8994",
  url="https://www.mdpi.com/2073-8994/10/11/611"
}