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Open AccessArticle

Hyperhomographies on Krasner Hyperfields

1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, 7718897111 Rafsanjan, Iran
2
Center for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia
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Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1442; https://doi.org/10.3390/sym11121442
Received: 18 October 2019 / Revised: 15 November 2019 / Accepted: 19 November 2019 / Published: 23 November 2019
In this paper, we introduce generalized homographic transformations as hyperhomographies over Krasner hyperfields.These particular algebraic hyperstructues are quotient structures of classical fields modulo normal groups. Besides, we define some hyperoperations and investigate the properties of the derived hypergroups and H v -groups associated with the considered hyperhomographies. They are equipped hyperhomographies obtained as quotient sets of nondegenerate hyperhomographies modulo a special equivalence. Thus the symmetrical property of the equivalence relations plays a fundamental role in this constructions. View Full-Text
Keywords: hypergroup; hyperring; hyperfield; (hyper)homography hypergroup; hyperring; hyperfield; (hyper)homography
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Vahedi, V.; Jafarpour, M.; Cristea, I. Hyperhomographies on Krasner Hyperfields. Symmetry 2019, 11, 1442.

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