Pre-semihyperadditive Categories

H. Shojaei; R. Ameri; S. Hoskova-Mayerova

doi:10.2478/auom-2019-0014

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Pre-semihyperadditive Categories

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 27 (2019): Issue 1 (March 2019)

By: H. Shojaei, R. Ameri and S. Hoskova-Mayerova

Open Access

|Mar 2019

Abstract

In this paper we extend the notion of classical (pre-)semiadditive category to (pre-)semihyperadditive category. Algebraic hyperstructures are algebraic systems whose objects possessing the hyperoperations or multi-valued operation. We introduce categories in which for objects A and B, the class of all morphisms from A to B denoted by Mor(A, B), admits an algebraic hyperstructures, such as semihypergroup or hypergroup. In this regards we introduce the various types of pre-semihyperadditive categories. Also, we construct some (pre-)semihyperadditive categories by introducing a class of hypermodules named general Krasner hypermodules. Finally, we investigate some properties of these categories.

References

[1] R. Ameri, On categories of hypergroups and hypermodules, Journal of Discrete Mathematical Sciences and Cryptography, 6(2-3) (2003), 121–132.10.1080/09720529.2003.10697969
Search in Google Scholar Back to article
[2] S. Awodey, Category theory, Oxford University Press, 2010.
Search in Google Scholar Back to article
[3] J. Chvalina, S. Hoskova-Mayerova, A. Deghan Nezhad, General actions of hypergroups and some applications, An. Stiint. Univ. “Ovidius” Constanta Ser. Mat., 21(1), (2013), 59–82.10.2478/auom-2013-0004
Search in Google Scholar Back to article
[4] J. Chvalina and S. Hoskova-Mayerova, On certain proximities and preorderings on the transposition hypergroups of linear first-order partial differential operators, An. Stiint. Univ. “Ovidius” Constanta Ser. Mat., 22(1), (2014), 85–103.10.2478/auom-2014-0008
Search in Google Scholar Back to article
[5] J. Chvalina, Š. Křehlík, M. Novák, Cartesian composition and the problem of generalizing the MAC condition to quasi- multiautomata. An. Stiint. Univ. ”Ovidius” Constanta Ser. Mat., 24(3), (2016), 79–100.10.1515/auom-2016-0049
Search in Google Scholar Back to article
[6] P. Corsini, Prolegomena of Hypergroup Theory, Second edition, Aviani Editore, Tricesimo, 1993.
Search in Google Scholar Back to article
[7] P. Corsini, V. Leoreanu, Application of Hyperstructure Theory, Kluwer Academic Pub., 2003.10.1007/978-1-4757-3714-1
Search in Google Scholar Back to article
[8] J. Chvalina, S. Hoskova-Mayerova, A. Deghan Nezhad, General actions of hypergroups and some applications, An. Stiint. Univ. “Ovidius” Constanta, Ser. Matematica, 21(1), 2013, 59–82.10.2478/auom-2013-0004
Search in Google Scholar Back to article
[9] J. Chvalina, S. Hoskova-Mayerova, On certain proximities and preorderings on the transposition hypergroups of linear first-order partial differential operators, An. Stiint. Univ. “Ovidius” Constanta, Ser. Matematica, 22(1), 2014, 1224–1784.10.2478/auom-2014-0008
Search in Google Scholar Back to article
[10] I. Cristea and S. Jancic-Rasovic, Compositions Hyperrings, An. Stiint. Univ. “Ovidius” Constanta Ser. Mat., 21(2), (2013), 81–94.10.2478/auom-2013-0024
Search in Google Scholar Back to article
[11] I. Cristea, Regularity of Intuitionistic Fuzzy Relations on Hypergroupoids, An. Stiint. Univ. “Ovidius” Constanta Ser. Mat., 22(1), (2014), 105–119.10.2478/auom-2014-0009
Search in Google Scholar Back to article
[12] I. Cristea and S. Hoskova, Fuzzy pseudotopological hypergroupoids, Iran. J. Fuzzy Syst., 6(4), (2009), 11–19.
Search in Google Scholar Back to article
[13] H. Aghabozorghi, I. Cristea, M. Jafarpour, On complementable semihypergroups, Comm. Algebra, 44(4) (2016), 1740–1753.10.1080/00927872.2015.1027395
Search in Google Scholar Back to article
[14] M. Norouzi and I. Cristea, A note on composition (m,n)-hyperrings, An. Stiint. Univ. ”Ovidius” Constanta Ser. Mat., 25(2) (2017).10.1515/auom-2017-0023
Search in Google Scholar Back to article
[15] S. Hoskova, Topological hypergroupoids, Comput. Math. Appl., 64(9)(2012), 2845–2849.10.1016/j.camwa.2012.04.017
Search in Google Scholar Back to article
[16] B. Davvaz, A brief survey of the theory of H_v-structures, 8^th AHA, Greece, Spanidis (2003), 39–70.
Search in Google Scholar Back to article
[17] B. Davvaz, Polygroup theory and related systems, World Sci. Publ., 2013.10.1142/8593
Search in Google Scholar Back to article
[18] B. Davvaz, V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007.
Search in Google Scholar Back to article
[19] M. Gondran and M. Minoux. Graphs, dioids and semirings, Operations Research/Computer Science Interfaces Series. 41, Springer, New York, 2008.
Search in Google Scholar Back to article
[20] M. Krasner, A class of hyperrings and hyperfields, International Journal of Mathematics and Mathematical Sciences 6(2), (1983), 307–311.10.1155/S0161171283000265
Search in Google Scholar Back to article
[21] Ch. G. Massouros, Free and cyclic hypermodules, Annali di Matematica Pura ed Applicata 150.1 (1988), 153–166.10.1007/BF01761468
Search in Google Scholar Back to article
[22] Ch. G. Massouros, On the theory of hyperrings and hyperfields, Algebra i Logika, 24 (1985), 728–742.10.1007/BF01978850
Search in Google Scholar Back to article
[23] F. Marty, Sur uni generalization de la notion de group, in: 8^th Congress Math. Scandenaves, Stockholm, (1934), 45–49.
Search in Google Scholar Back to article
[24] M. Novák, n-ary hyperstructures constructed from binary quasi-orderer semigroups, An. Stiint. Univ. “Ovidius” Constanta Ser. Mat., 22(3), (2014), 147–168.10.2478/auom-2014-0056
Search in Google Scholar Back to article
[25] M. Novák, Ordering in the Algebraic Hyperstructure Theory: Some Examples with a Potential for Applications in Social Sciences. In Models and Theories in Social Systems. Studies in Systems, Decision and Control. Cham, Switzerland: Springer, 2018, 535-551. ISBN: 978-3-030-00083-7.10.1007/978-3-030-00084-4_28
Search in Google Scholar Back to article
[26] M. Novák, Křehlik, Š., Cristea, I,. Cyclicity in EL-hypergroups. Symmetry, 2018, 10(11), 1–13.10.3390/sym10110611
Search in Google Scholar Back to article
[27] M. Novák, Ovaliadis, K.; Křehlik, Š., A hyperstructure model of underwater wireless sensor network (UWSN) design. In International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2017). AIP conference proceedings. 1978. Thessaloniki, Greece: American Institute of Physics, 2018. p. 340006-1 (340006-4 p.) ISBN: 978-0-7354-1690-1. ISSN: 0094-243X.10.1063/1.5043949
Search in Google Scholar Back to article
[28] M. Novák, Křehlik, Š., EL-hyperstructures revisited. Soft Computing, 21, 2018, 7269–7680.10.1007/s00500-017-2728-y
Search in Google Scholar Back to article
[29] H. Shojaei, R. Ameri, Some results on categories of krasner hypermodules, J. Fundam. Appl. Sci., 8(3S) (2016), 2298–2306.
Search in Google Scholar Back to article
[30] H. Shojaei, R. Ameri and S. Hoskova-Mayerova, On Properties of Various Morphisms in The Categories of General Krasner Hypermodules. Italian J. of Pure and Applied Math., 39 2018, p. 475–484.
Search in Google Scholar Back to article
[31] H. Shojaei, R. Ameri and S. Hoskova-Mayerova, Some properties of morphisms of RG.mod as an i1-PSHA Category In: AIP Conference Proceedings 1978 T. Simos and Ch. Tsitouras (Eds.). USA: AIP Publishing, 2018, p. 4. ISBN 978-0-7354-1690-1.10.1063/1.5043948
Search in Google Scholar Back to article
[32] O. Viro, Hyperfields for tropical geometry I. hyperfields and dequantization. Preprint, arXiv., (2010), 1006–3034.
Search in Google Scholar Back to article
[33] T. Vougiouklis, Hyperstructures and their Representations, Monographs in Mathematics, Hadronic, 1994.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2019-0014 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 269 - 288

Submitted on: Jul 25, 2017

Accepted on: Jan 27, 2018

Published on: Mar 2, 2019

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Pre-semihyperadditive Category,

Pre-hyperadditive Category,

Pre-canonical Hyperadditive Category,

Hypercategory

Related subjects:

Mathematics,

General mathematics

© 2019 H. Shojaei, R. Ameri, S. Hoskova-Mayerova, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 27 (2019): Issue 1 (March 2019)