Weak Embeddable Hypernear-Rings
In this paper we extend one of the main problems of near-rings to the framework of algebraic hypercompositional structures. This problem states that every near-ring is isomorphic with a near-ring of the transformations of a group. First we endow the set of all multitransformations of a hypergroup (n...
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MDPI AG
2019-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/8/964 |
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doaj-ce9b874042684b469519e905ec97de052020-11-24T21:29:15ZengMDPI AGSymmetry2073-89942019-08-0111896410.3390/sym11080964sym11080964Weak Embeddable Hypernear-RingsJelena Dakić0Sanja Jančić-Rašović1Irina Cristea2Department of Mathematics, Faculty of Natural Science and Mathematics, University of Montenegro, 81000 Podgorica, MontenegroDepartment of Mathematics, Faculty of Natural Science and Mathematics, University of Montenegro, 81000 Podgorica, MontenegroCentre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, SloveniaIn this paper we extend one of the main problems of near-rings to the framework of algebraic hypercompositional structures. This problem states that every near-ring is isomorphic with a near-ring of the transformations of a group. First we endow the set of all multitransformations of a hypergroup (not necessarily abelian) with a general hypernear-ring structure, called the multitransformation general hypernear-ring associated with a hypergroup. Then we show that any hypernear-ring can be weakly embedded into a multitransformation general hypernear-ring, generalizing the similar classical theorem on near-rings. Several properties of hypernear-rings related with this property are discussed and illustrated also by examples.https://www.mdpi.com/2073-8994/11/8/964hypernear-ringmultitransformationembedding |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jelena Dakić Sanja Jančić-Rašović Irina Cristea |
| spellingShingle |
Jelena Dakić Sanja Jančić-Rašović Irina Cristea Weak Embeddable Hypernear-Rings Symmetry hypernear-ring multitransformation embedding |
| author_facet |
Jelena Dakić Sanja Jančić-Rašović Irina Cristea |
| author_sort |
Jelena Dakić |
| title |
Weak Embeddable Hypernear-Rings |
| title_short |
Weak Embeddable Hypernear-Rings |
| title_full |
Weak Embeddable Hypernear-Rings |
| title_fullStr |
Weak Embeddable Hypernear-Rings |
| title_full_unstemmed |
Weak Embeddable Hypernear-Rings |
| title_sort |
weak embeddable hypernear-rings |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2019-08-01 |
| description |
In this paper we extend one of the main problems of near-rings to the framework of algebraic hypercompositional structures. This problem states that every near-ring is isomorphic with a near-ring of the transformations of a group. First we endow the set of all multitransformations of a hypergroup (not necessarily abelian) with a general hypernear-ring structure, called the multitransformation general hypernear-ring associated with a hypergroup. Then we show that any hypernear-ring can be weakly embedded into a multitransformation general hypernear-ring, generalizing the similar classical theorem on near-rings. Several properties of hypernear-rings related with this property are discussed and illustrated also by examples. |
| topic |
hypernear-ring multitransformation embedding |
| url |
https://www.mdpi.com/2073-8994/11/8/964 |
| work_keys_str_mv |
AT jelenadakic weakembeddablehypernearrings AT sanjajancicrasovic weakembeddablehypernearrings AT irinacristea weakembeddablehypernearrings |
| _version_ |
1725966538549231616 |