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@article{1465756,
author = {Novák, Michal and Křehlík, Štěpán and Cristea, Irina},
article_location = {Basel},
article_number = {11},
doi = {http://dx.doi.org/10.3390/sym10110611},
keywords = {cyclic group; cyclic hypergroup; EL-hyperstructure; preorder},
language = {eng},
issn = {2073-8994},
journal = {Symmetry},
title = {Cyclicity in EL-hypergroups},
url = {https://www.mdpi.com/2073-8994/10/11/611},
volume = {10},
year = {2018}
}
TY - JOUR
ID - 1465756
AU - Novák, Michal - Křehlík, Štěpán - Cristea, Irina
PY - 2018
TI - Cyclicity in EL-hypergroups
JF - Symmetry
VL - 10
IS - 11
SP - 1-13
EP - 1-13
PB - MDPI
SN - 20738994
KW - cyclic group
KW - cyclic hypergroup
KW - EL-hyperstructure
KW - preorder
UR - https://www.mdpi.com/2073-8994/10/11/611
L2 - https://www.mdpi.com/2073-8994/10/11/611
N2 - 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.
ER -
NOVÁK, Michal, Štěpán KŘEHLÍK and Irina CRISTEA. Cyclicity in EL-hypergroups. \textit{Symmetry}. Basel: MDPI, 2018, vol.~10, No~11, p.~1-13. ISSN~2073-8994. doi:10.3390/sym10110611.
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