An organized and constantly updated list of references on hypercompositional algebra and related topics :
Origins
- Marty, Frédéric. Sur une généralization de la notion de groupe, in Huitiéme Congrès des Mathématiciens Scandenaves Stockholm. 45-49 (1934)
- Dresher, Melvin and Ore, Oystein. Theory of Multigroups. Amer. J. Math. 60(3) Johns Hopkins University Press. 705-733 (1938)
Join spaces and transpositions hypergroups
- Prenowitz, Walter and Jantosciak, James. Geometries and join spaces. J. Reine Angew. Math. 257 Walter de Gruyter. 100-128 (1972)
- Jantosciak, James. Transposition hypergroups: noncommutative join spaces. J. Algebra 187(1) Elsevier. 97-119 (1997) -- DOI link
Hyperoperations associated to graphs
- Kalampakas, Antonios and Spartalis, Stefanos and Tsigkas, Alexandros. The path hyperoperation. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica 22(1), 141-153 (2014) -- DOI link
- Kalampakas, Antonios and Spartalis, Stefanos. Path hypergroupoids: commutativity and graph connectivity. European Journal of Combinatorics 44(PB), 257-264 (2015) -- DOI link
- Kalampakas, Antonios and Spartalis, Stefanos. Hyperoperations on directed graphs. Journal of Discrete Mathematical Sciences and Cryptography 27(3), 1011-1025 (2024) -- DOI link
Canonical hypergroups and polygroups
- Mittas, Jean. Hypergroupes canoniques valués et hypervalués. Math. Balkanica 1, Bulgarian Academy of Sciences 181–185 (1971)
- Mittas, Jean. Hypergroupes canoniques. Math. Balkanica 2, Bulgarian Academy of Sciences 165-179 (1972)
- Comer, Stephen D. Combinatorial aspects of relations. Algebra Universalis 18(1) Springer-Verlag. 77-94 (1984) -- DOI link
- Linzi, Alessandro. Polygroup objects in regular categories. AIMS Mathematics 9(5) 11247-11277 (2024) -- DOI link
Krasner hyperfields and hyperrings
- Krasner, Marc. Approximation des corps valués complets de caractéristique p≠0 par ceux de caractéristique 0, in Colloque d'algèbre supérieure, tenu à Bruxelles du 19 au 22 décembre 1956. 129-206 (1957)
- Krasner, Marc. A class of hyperrings and hyperfields. Internat. J. Math. Math. Sci. 6(2) Hindawi. 307-311 (1983) -- DOI link
- Massouros, Christos. Methods of constructing hyperfields. Internat. J. Math. Math. Sci. 8(4) Hindawi. 725-728 (1985) -- DOI link
- Mittas, Jean. Sur les hyperanneaux et les hypercorps. Math. Balkanica 3, Bulgarian Academy of Sciences 368-382 (1973)
- Gładki, Paweł and Marshall, Murray. Orderings and signatures of higher level on multirings and hyperfields. J. K-Theory 10(3) Cambridge University Press (2012) -- DOI link
- Kuhlmann, Katarzyna & Linzi, Alessandro & Stojałowska, Hanna. Orderings and valuations in hyperfields. J. Algebra 611 Elsevier. 399-421 (2022) -- DOI link
- Kȩdzierski, Dawid Edmund & Linzi, Alessandro & Stojałowska, Hanna. Characteristic, C-Characteristic and Positive Cones in Hyperfields. Mathematics 11(3), 779 MDPI (2023) -- DOI link
- Linzi, Alessandro. A result of Krasner in categorial form. Mathematics 11(24), 4923 MDPI (2023) -- DOI link
Enumeration
- Ameri, R. and Eyvazi, M. and Hoskova-Mayerova, S. Advanced results in enumeration of hyperfields. AIMS Math. 5(6) 6552-6579 (2020) -- DOI link
- Cristea, Irina and Jafarpour, Morteza and Mousavi, Seyed S. and Soleymani, Ali Enumeration of Rosenberg hypergroups. Comput. Math. Appl. 60(10) 2753-2763 (2010) -- DOI link
- Tsitouras, Ch. and Massouros, Ch. G. On enumeration of hypergroups of order 3. Comput. Math. Appl. 59(1) 519-523 (2010) -- DOI link
Hypergroups and Dependence relations
- Cristea, Irina and Kocijan, Juš and Novák, Michal. Introduction to Dependence Relations and Their Links to Algebraic Hyperstructures. Mathematics 7(10), 885 MDPI (2019) -- DOI link
- Linzi, Alessandro & Cristea, Irina. Dependence Relations and Grade Fuzzy Set. Symmetry 15(2), 311 MDPI (2023) -- DOI link
Books
- Prenowitz, Walter and Jantosciak, James. Join geometries. Undergraduate Texts in Mathematics. Springer-Verlag. New York-Heidelberg (1979)
- Corsini, Piergiulio. Prolegomena of hypergroup theory. Aviani Editore, Tricesimo (1992)
- Corsini, Piergiulio and Leoreanu, Violeta. Applications of hyperstructure theory. Advances in Mathematics. Springer, New York (2010) -- DOI link
Surveys
- Golzio, Ana Claudia. A brief historical survey on hyperstructures in algebra and logic. South Amer. J. Log. 4(1) ISSN: 2446-6719 -- OA link
- Massouros, Christos & Massouros, Gerasimos. An Overview of the Foundations of the Hypergroup Theory. Mathematics 9(9), 1014 MDPI (2021) -- DOI link