Publication detail

Cyclicity in EL-hypergroups

NOVÁK, M. KŘEHLÍK, Š. CRISTEA, I.

Original Title

Cyclicity in EL-hypergroups

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

cyclic group; cyclic hypergroup; EL-hyperstructure; preorder

Authors

NOVÁK, M.; KŘEHLÍK, Š.; CRISTEA, I.

Released

7. 11. 2018

Publisher

MDPI

ISBN

2073-8994

Periodical

Symmetry

Year of study

10

Number

11

State

Swiss Confederation

Pages from

1

Pages to

13

Pages count

13

URL

Full text in the Digital Library

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"
}