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Open AccessArticle

Weak Embeddable Hypernear-Rings

1
Department of Mathematics, Faculty of Natural Science and Mathematics, University of Montenegro, 81000 Podgorica, Montenegro
2
Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(8), 964; https://doi.org/10.3390/sym11080964
Received: 28 June 2019 / Revised: 15 July 2019 / Accepted: 18 July 2019 / Published: 1 August 2019
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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PDF [249 KB, uploaded 1 August 2019]

Abstract

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. View Full-Text
Keywords: hypernear-ring; multitransformation; embedding hypernear-ring; multitransformation; embedding
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Dakić, J.; Jančić-Rašović, S.; Cristea, I. Weak Embeddable Hypernear-Rings. Symmetry 2019, 11, 964.

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