The Reducibility Concept in General Hyperrings

Irina Cristea and Milica Kankaraš
Additional contact information
Irina Cristea: Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia
Milica Kankaraš: Department of Mathematics, University of Montenegro, 81000 Podgorica, Montenegro

Mathematics, 2021, vol. 9, issue 17, 1-14

Abstract: By using three equivalence relations, we characterize the behaviour of the elements in a hypercompositional structure. With respect to a hyperoperation, some elements play specific roles: their hypercomposition with all the elements of the carrier set gives the same result; they belong to the same hypercomposition of elements; or they have both properties, being essentially indistinguishable. These equivalences were first defined for hypergroups, and here we extend and study them for general hyperrings—that is, structures endowed with two hyperoperations. We first present their general properties, we define the concept of reducibility, and then we focus on particular classes of hyperrings: the hyperrings of formal series, the hyperrings with P -hyperoperations, complete hyperrings, and ( H , R ) -hyperrings. Our main aim is to find conditions under which these hyperrings are reduced or not.

Keywords: general hyperring; reducibility; fundamental relation; equivalence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/17/2037/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/17/2037/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:17:p:2037-:d:621076

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().