View More View Less
  • 1 Yazd University Department of Mathematics Yazd Iran
Open access

This paper attempts an exposition of the connection between valuation theory and hyperstructure theory. In this regards, by considering the notion of totally ordered canonical hypergroup we define a hypervaluation of a hyperfield onto a totally ordered canonical hypergroup and obtain some related basic results.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Alajbegovic, J. and Mockor, J., Valuations on multirings, Comm. Math. Univ. St. Pauli (Tokyo), 34 (1985), 201–225.

    Mockor J. , 'Valuations on multirings ' (1985 ) 34 Comm. Math. Univ. St. Pauli (Tokyo) : 201 -225.

    • Search Google Scholar
  • Alajbegovic, J. and Mockor, J., Approximation Theorems in Commutative Algebra: Classical and Categorical Methods, Kluwer Academic Publishers, (1992).

    Mockor J. , '', in Approximation Theorems in Commutative Algebra: Classical and Categorical Methods , (1992 ) -.

    • Search Google Scholar
  • Bonansinga, P., Quasicanonical hypergroups, (Italian), Atti Soc. Peloritana Sci. Fis. Mat. Natur., 27 (1981), 9–17.

    Bonansinga P. , 'Quasicanonical hypergroups, (Italian) ' (1981 ) 27 Atti Soc. Peloritana Sci. Fis. Mat. Natur. : 9 -17.

    • Search Google Scholar
  • Bonansinga, P., Weakly quasicanonical hypergroups, (Italian), Atti Sem. Mat. Fis. Univ. Modena, 30 (1981), 286–298.

    Bonansinga P. , 'Weakly quasicanonical hypergroups, (Italian) ' (1981 ) 30 Atti Sem. Mat. Fis. Univ. Modena : 286 -298.

    • Search Google Scholar
  • Bourbaki, N., Alébre commutative, Hermann, Paris, (1964).

    Bourbaki N. , '', in Alébre commutative , (1964 ) -.

  • Corsini, P., Prolegomena of Hypergroup Theory, Second edition, Aviani editor, (1993).

    Corsini P. , '', in Prolegomena of Hypergroup Theory , (1993 ) -.

  • Corsini, P. and Leoreanu, V., Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publishers, (2003).

    Leoreanu V. , '', in Applications of Hyperstructure Theory , (2003 ) -.

  • Corsini, P., Finite canonical hypergroups with partial scalar identities, (Italian), Rend. Circ. Mat. Palermo (2), 36 (1987), 205–219.

    Corsini P. , 'Finite canonical hypergroups with partial scalar identities, (Italian) ' (1987 ) 36 Rend. Circ. Mat. Palermo (2) : 205 -219.

    • Search Google Scholar
  • Corsini, P., Feebly canonical and 1-hypergroups, Acta Universitatis Carolinae, Math. et Phys., vol. 24, no. 2, (1983).

  • Corsini, P. and Bonansinga, P., Sugli omomorfismi di semi-ipergruppi e di ipergruppi, B.U.M.I., 1-B, (1982).

    Bonansinga P. , '', in Sugli omomorfismi di semi-ipergruppi e di ipergruppi , (1982 ) -.

  • Cristea, I. and Jančić-Rašović, S., Composition hyperrings, An Stiint Univ. “Ovidius” Constanta Ser. Mat., 21 no 2 (2013), 81–94.

    Jančić-Rašović S. , 'Composition hyperrings ' (2013 ) 21 An Stiint Univ. “Ovidius” Constanta Ser. Mat. : 81 -94.

    • Search Google Scholar
  • Davvaz, B. and Leoreanu-Fotea, V., Hyperring Theory and Applications, International Academic Press, 115, Palm Harber, USA, (2007).

    Leoreanu-Fotea V. , '', in Hyperring Theory and Applications , (2007 ) -.

  • Davvaz, B., Polygroup Theory and Related Systems, World Scientific Publishing, (2013).

    Davvaz B. , '', in Polygroup Theory and Related Systems , (2013 ) -.

  • De Salvo, M., Feebly canonical hypergroups, Graphs, designs and combinatorial geometries, (Catania), J. Combin, Inform, System Sci., 15 (1990), 133–150.

    Salvo M. , 'Feebly canonical hypergroups, Graphs, designs and combinatorial geometries, (Catania) ' (1990 ) 15 J. Combin, Inform, System Sci. : 133 -150.

    • Search Google Scholar
  • Davvaz, B. and Salasi, A., A realization of hyperrings, Comm. Algebra, 34 (12) (2006), 4389–4400.

    Salasi A. , 'A realization of hyperrings ' (2006 ) 34 Comm. Algebra : 4389 -4400.

  • Endler, O., Valuation theory, Springer, Berlin-Heidelberg-New York, (1972).

    Endler O. , '', in Valuation theory , (1972 ) -.

  • Engler, A. J. and Prestel, A., Valued fields, Springer, (2005).

    Prestel A. , '', in Valued fields , (2005 ) -.

  • Hasse, H., zwei existenztheoreme über algebraische zahlkörper, Math. Ann., 95 (1925), 229–238.

    Hasse H. , 'zwei existenztheoreme über algebraische zahlkörper ' (1925 ) 95 Math. Ann. : 229 -238.

    • Search Google Scholar
  • Kemprasit, Y., Multiplicative interval semigroups on R admitting hyperring structure, Ital. J. Pure Appl. Math., 11 (2002), 205–212.

    Kemprasit Y. , 'Multiplicative interval semigroups on R admitting hyperring structure ' (2002 ) 11 Ital. J. Pure Appl. Math. : 205 -212.

    • Search Google Scholar
  • Konstantinidou, M. and Serafimidis, K., Sur les filets des hypergroupes canoniques strictement réliculés, (French) [Threads of strictly lattice-ordered canonical hypergroups], Riv. Mat. Univ. Parma, (4) 13 (1987), 67–72.

    Serafimidis K. , 'Sur les filets des hypergroupes canoniques strictement réliculés, (French) [Threads of strictly lattice-ordered canonical hypergroups] ' (1987 ) 13 Riv. Mat. Univ. Parma : 67 -72.

    • Search Google Scholar
  • Krasner, M., A class of hyperrings and hyperfields, Int. J. Math and Math. Sci., 2 (1983), 307–312.

    Krasner M. , 'A class of hyperrings and hyperfields ' (1983 ) 2 Int. J. Math and Math. Sci. : 307 -312.

    • Search Google Scholar
  • Krasner, M., Approximation des corps valués complets de caractéristique p, p > 0, par ceux de caractéristique zero, Colloque d’ Algbre Supérieure, Bruxelles, (1957).

    Krasner M. , '', in Approximation des corps valués complets de caractéristique p, p > 0, par ceux de caractéristique zero , (1957 ) -.

    • Search Google Scholar
  • Krull, W., Allgemeine Bewertungstheorie, J. reine angew. Math., 167 (1932), 160–196.

    Krull W. , 'Allgemeine Bewertungstheorie ' (1932 ) 167 J. reine angew. Math. : 160 -196.

  • Kürschák, J., Über Limesbildung und allgemeine Körpertheorie, Proceedings of the 5th International Congress of Mathematicians Cambridge 1912, vol. 1 (1913), 285–289.

    Kürschák J. , 'Über Limesbildung und allgemeine Körpertheorie ' (1913 ) 1 Proceedings of the 5th International Congress of Mathematicians Cambridge 1912 : 285 -289.

    • Search Google Scholar
  • Marty, F., Sur une generalization de la notion de group, 8th congress Math. Scandenaves, Stockholm, (1934), 45–49.

    Marty F. , '', in Sur une generalization de la notion de group , (1934 ) -.

  • Mittas, J., Hypergroupes canoniques hypervalués, (French), C.R. Acad. Sci. Paris Sér, A-B, 271 (1970), A4–A7.

    Mittas J. , 'Hypergroupes canoniques hypervalués, (French) ' (1970 ) 271 C.R. Acad. Sci. Paris Sér, A-B : A4 -A7.

    • Search Google Scholar
  • Mittas, J., Hypergroupes canoniques valués et hypervalués, (French), Math. Balkanica, 1 (1971), 181–185.

    Mittas J. , 'Hypergroupes canoniques valués et hypervalués, (French) ' (1971 ) 1 Math. Balkanica : 181 -185.

    • Search Google Scholar
  • Mittas, J., Hypergroupes canoniques, Math. Balkanica, Beograd, 2 (1972), 165–179.

    Mittas J. , 'Hypergroupes canoniques ' (1972 ) 2 Math. Balkanica, Beograd : 165 -179.

  • Nakassis, A., Recent results in hyperring and hyperfield theory, Internat. J. Math. Math. Sci., 11 no. 2 (1988), 209–220.

    Nakassis A. , 'Recent results in hyperring and hyperfield theory ' (1988 ) 11 Internat. J. Math. Math. Sci. : 209 -220.

    • Search Google Scholar
  • Ostrowski, A., Untersuchungen zur arithmetischen theorie der körper, Math. Z., 39 (1934) 269–404.

    Ostrowski A. , 'Untersuchungen zur arithmetischen theorie der körper ' (1934 ) 39 Math. Z. : 269 -404.

    • Search Google Scholar
  • Ribenboim, P., The Theory Of Classical Valuations, Springer-Verlag, (1999).

    Ribenboim P. , '', in The Theory Of Classical Valuations , (1999 ) -.

  • Samuel, P. and Zariski, O., Commutative algebra, I, II, Van Nostrand, Princeton, (1960).

    Zariski O. , '', in Commutative algebra , (1960 ) -.

  • Schilling, O. F. G., The theory of valuations, A.M.S. Math. Surveys, Nr. 4, Providence, Rhode Island, (1950).

    Schilling O. F. G. , '', in The theory of valuations , (1950 ) -.

  • Schmidt, F. K., Mehrfach perfekte Körper, Math. Annalen, 108 (1933), 1–25.

    Schmidt F. K. , 'Mehrfach perfekte Körper ' (1933 ) 108 Math. Annalen : 1 -25.

  • Serafimidis, K., Sur les hypergroups canoniques ordonnés et strictement ordonnés, (French) [Ordered and strictly ordered canonical hypergroups], Rend. Mat., (7) 6 (1986), 231–238.

    Serafimidis K. , 'Sur les hypergroups canoniques ordonnés et strictement ordonnés, (French) [Ordered and strictly ordered canonical hypergroups] ' (1986 ) 6 Rend. Mat. : 231 -238.

    • Search Google Scholar
  • Serafimidis, K., Konstantinidou, M. and Mittas, J., Sur les hypergroups canoniques strictement réticulés, (French) [On strictly lattice-ordered canonical hypergroups], Riv. Mat. Pura Appl., 2 (1987), 21–35.

    Mittas J. , 'Sur les hypergroups canoniques strictement réticulés, (French) [On strictly lattice-ordered canonical hypergroups] ' (1987 ) 2 Riv. Mat. Pura Appl. : 21 -35.

    • Search Google Scholar
  • Spartalis, S., A class of hyperrings, Riv. Mat. Pura Appl., No. 4 (1989), 55–64.

    Spartalis S. , 'A class of hyperrings ' (1989 ) 4 Riv. Mat. Pura Appl. : 55 -64.

  • Vougiouklis, T., Hyperstructures and their representations, Hadronic Press, Inc., 115, Palm Harber, USA, (1994).

    Vougiouklis T. , '', in Hyperstructures and their representations , (1994 ) -.

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE

 

  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • SCOPUS
  • The ISI Alerting Services

 

Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu