Araştırma Makalesi
BibTex RIS Kaynak Göster

Composition in $EL$-hyperstructures

Yıl 2019, Cilt: 48 Sayı: 1, 45 - 58, 01.02.2019

Öz

The link between ordered sets and hyperstructures is one of the classical areas of research in the hyperstructure theory. In this paper we focus on $EL$--hyperstructures, i.e. a class of hyperstructures constructed from quasi-ordered semigroups. In our paper we link this concept to the concept of a \emph{composition hyperring}, a recent hyperstructure generalization of the classical notion of a composition ring.

Kaynakça

  • I. Adler, Composition rings, Duke Math. J. 29, 607-623, 1962.
  • S. M. Anvariyeh and B. Davvaz, Strongly transitive geometric spaces associated to hypermodules, J. Algebra 332, 1340-1359, 2009.
  • J. Chvalina, Commutative hypergroups in the sense of Marty and ordered sets, General Algebra and Ordered Sets, Proc. Int. Conf. Olomouc, 19-30, 1994.
  • J. Chvalina, Functional Graphs, Quasi-ordered Sets and Commutative Hypergroups (in Czech), Masaryk University, Brno, 1995.
  • J. Chvalina and L. Chvalinová, Transposition hypergroups formed by transformation operators on rings of differentiable functions, Ital. J. Pure Appl. Math. 15, 93-106, 2004.
  • J. Chvalina, Š. Hošková-Mayerová and A.D. Nezhad, General actions of hyperstructures and some applications, An. St. Univ. Ovidius Constanta, 21 (1), 59-82, 2013.
  • A. Connes and C. Consani, The hyperring of adéle classes, J. Number Theory 131 (2), 159-194, 2011.
  • P. Corsini, Hyperstructures associated with ordered sets, Bull. Greek Math. Soc. 48, 7-18, 2003.
  • P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Kluwer Academic Publishers, Dodrecht, 2003.
  • I. Cristea and S. Jancic-Rašovic, Composition hyperrings, An. St. Univ. Ovidius Constanta 21 (2), 81-94, 2013.
  • B. Davvaz and V. Leoreanu Fotea, Applications of Hyperring Theory, International Academic Press, Palm Harbor, 2007.
  • B. Davvaz, N. Rakhsh-Khorshid and K.P. Shum, Construction of composition $(m,n,k)$-hyperrings, An. St. Univ. Ovidius Constanta 24 (1), 177-188, 2016.
  • B. Davvaz and A. Salasi, A realization of hyperrings, Comm. Algebra 34, 4389-4400, 2006.
  • A. Deghan Nezhad and B. Davvaz, An Introduction to the Theory of $H_v$-Semilattices, Bull. Malays. Math. Sci. Soc. 32 (3), 375-390, 2009.
  • S.H. Ghazavi and S.M. Anvariyeh, $EL$-hyperstructures associated to $n$-ary relations, Soft Comput. 21 (19), 5841-5850, 2017.
  • D. Heidari and B. Davvaz, On ordered hyperstructures, U.P.B. Sci. Bull. Series A, 73 (2), 2011.
  • K. Iwasava, On linearly ordered groups, J. Math. Soc. 1 (1), 1-9, 1948.
  • S. Jancic-Rašovic, About the hyperring of polynomials, Ital. J. Pure Appl. Math. 28, 223-234, 2007.
  • M. Krasner, A class of hyperrings and hyperfields, Int. J. Math. Sci. 6 (2), 307-312, 1983.
  • M. Krasner, Approximation des corps values complets de characteristique $p\not=0$ par ceux de characteristique 0, Colloque d’Algebre Superieure, CBRM, Bruxelles, 1957.
  • Š. Krehlík and M. Novák, From lattices to $H_v$-matrices, An. St. Univ. Ovidius Constanta 24 (3), 209-222, 2016.
  • Ch.G. Massouros, On the theory of hyperrings and hyperfields, Algebra i Logika 24 (6), 728-742, 1985.
  • G.G. Massouros, The hyperringoid, Multiple Valued Logic 3, 217-234, 1998.
  • Ch.G. Massouros and G.G. Massouros, On join hyperrings, Proceedings of the 10th International Congress on Algebraic Hyperstructures and Applications, Brno, Czech Republic, 203-215, 2009.
  • Ch.G. Massouros and G. G. Massouros, The transposition axiom in hypercompositional structures, Ratio Mathematica 21, 75-90, 2011.
  • S. Mirvakili and B. Davvaz, Applications of the $a^{\ast}$-relation to Krasner hyperrings, J. Algebra 362, 145-156, 2012.
  • J.D. Mittas, Sur certaines classes de structures hypercompositionnelles, Proceedings of the Academy of Athens, 48, 298-318, 1973.
  • A. Nakasis, Recent results in hyperring and hyperfield theory, Internat. J. of Math. & Math. Sci. 11 (2), 209-220, 1988.
  • M. Novák, Some basic properties of $EL$-hyperstructures, European J. Combin. 34, 446-459, 2013.
  • M. Novák, Potential of the “Ends lemma" to create ring-like hyperstructures from quasi-ordered (semi)groups, South Bohemia Mathem. Letters 17 (1), 39-50, 2009.
  • M. Novák, On $EL$-semihypergroups, European J. Combin. 44 Part B, 274-286, 2015.
  • S. Spartalis, A class of hyperrings, Riv. Mat. Pura Appl. 4, 55-64, 1989.
  • Th. Vougiouklis, On some representations of hypergroups, Annales scientifiques de l’Université de Clermont-Ferrand 2, Série Mathematiques 26, 21-29, 1990.
Yıl 2019, Cilt: 48 Sayı: 1, 45 - 58, 01.02.2019

Öz

Kaynakça

  • I. Adler, Composition rings, Duke Math. J. 29, 607-623, 1962.
  • S. M. Anvariyeh and B. Davvaz, Strongly transitive geometric spaces associated to hypermodules, J. Algebra 332, 1340-1359, 2009.
  • J. Chvalina, Commutative hypergroups in the sense of Marty and ordered sets, General Algebra and Ordered Sets, Proc. Int. Conf. Olomouc, 19-30, 1994.
  • J. Chvalina, Functional Graphs, Quasi-ordered Sets and Commutative Hypergroups (in Czech), Masaryk University, Brno, 1995.
  • J. Chvalina and L. Chvalinová, Transposition hypergroups formed by transformation operators on rings of differentiable functions, Ital. J. Pure Appl. Math. 15, 93-106, 2004.
  • J. Chvalina, Š. Hošková-Mayerová and A.D. Nezhad, General actions of hyperstructures and some applications, An. St. Univ. Ovidius Constanta, 21 (1), 59-82, 2013.
  • A. Connes and C. Consani, The hyperring of adéle classes, J. Number Theory 131 (2), 159-194, 2011.
  • P. Corsini, Hyperstructures associated with ordered sets, Bull. Greek Math. Soc. 48, 7-18, 2003.
  • P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Kluwer Academic Publishers, Dodrecht, 2003.
  • I. Cristea and S. Jancic-Rašovic, Composition hyperrings, An. St. Univ. Ovidius Constanta 21 (2), 81-94, 2013.
  • B. Davvaz and V. Leoreanu Fotea, Applications of Hyperring Theory, International Academic Press, Palm Harbor, 2007.
  • B. Davvaz, N. Rakhsh-Khorshid and K.P. Shum, Construction of composition $(m,n,k)$-hyperrings, An. St. Univ. Ovidius Constanta 24 (1), 177-188, 2016.
  • B. Davvaz and A. Salasi, A realization of hyperrings, Comm. Algebra 34, 4389-4400, 2006.
  • A. Deghan Nezhad and B. Davvaz, An Introduction to the Theory of $H_v$-Semilattices, Bull. Malays. Math. Sci. Soc. 32 (3), 375-390, 2009.
  • S.H. Ghazavi and S.M. Anvariyeh, $EL$-hyperstructures associated to $n$-ary relations, Soft Comput. 21 (19), 5841-5850, 2017.
  • D. Heidari and B. Davvaz, On ordered hyperstructures, U.P.B. Sci. Bull. Series A, 73 (2), 2011.
  • K. Iwasava, On linearly ordered groups, J. Math. Soc. 1 (1), 1-9, 1948.
  • S. Jancic-Rašovic, About the hyperring of polynomials, Ital. J. Pure Appl. Math. 28, 223-234, 2007.
  • M. Krasner, A class of hyperrings and hyperfields, Int. J. Math. Sci. 6 (2), 307-312, 1983.
  • M. Krasner, Approximation des corps values complets de characteristique $p\not=0$ par ceux de characteristique 0, Colloque d’Algebre Superieure, CBRM, Bruxelles, 1957.
  • Š. Krehlík and M. Novák, From lattices to $H_v$-matrices, An. St. Univ. Ovidius Constanta 24 (3), 209-222, 2016.
  • Ch.G. Massouros, On the theory of hyperrings and hyperfields, Algebra i Logika 24 (6), 728-742, 1985.
  • G.G. Massouros, The hyperringoid, Multiple Valued Logic 3, 217-234, 1998.
  • Ch.G. Massouros and G.G. Massouros, On join hyperrings, Proceedings of the 10th International Congress on Algebraic Hyperstructures and Applications, Brno, Czech Republic, 203-215, 2009.
  • Ch.G. Massouros and G. G. Massouros, The transposition axiom in hypercompositional structures, Ratio Mathematica 21, 75-90, 2011.
  • S. Mirvakili and B. Davvaz, Applications of the $a^{\ast}$-relation to Krasner hyperrings, J. Algebra 362, 145-156, 2012.
  • J.D. Mittas, Sur certaines classes de structures hypercompositionnelles, Proceedings of the Academy of Athens, 48, 298-318, 1973.
  • A. Nakasis, Recent results in hyperring and hyperfield theory, Internat. J. of Math. & Math. Sci. 11 (2), 209-220, 1988.
  • M. Novák, Some basic properties of $EL$-hyperstructures, European J. Combin. 34, 446-459, 2013.
  • M. Novák, Potential of the “Ends lemma" to create ring-like hyperstructures from quasi-ordered (semi)groups, South Bohemia Mathem. Letters 17 (1), 39-50, 2009.
  • M. Novák, On $EL$-semihypergroups, European J. Combin. 44 Part B, 274-286, 2015.
  • S. Spartalis, A class of hyperrings, Riv. Mat. Pura Appl. 4, 55-64, 1989.
  • Th. Vougiouklis, On some representations of hypergroups, Annales scientifiques de l’Université de Clermont-Ferrand 2, Série Mathematiques 26, 21-29, 1990.
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Michal Novak Bu kişi benim

Irina Cristea Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 48 Sayı: 1

Kaynak Göster

APA Novak, M., & Cristea, I. (2019). Composition in $EL$-hyperstructures. Hacettepe Journal of Mathematics and Statistics, 48(1), 45-58.
AMA Novak M, Cristea I. Composition in $EL$-hyperstructures. Hacettepe Journal of Mathematics and Statistics. Şubat 2019;48(1):45-58.
Chicago Novak, Michal, ve Irina Cristea. “Composition in $EL$-Hyperstructures”. Hacettepe Journal of Mathematics and Statistics 48, sy. 1 (Şubat 2019): 45-58.
EndNote Novak M, Cristea I (01 Şubat 2019) Composition in $EL$-hyperstructures. Hacettepe Journal of Mathematics and Statistics 48 1 45–58.
IEEE M. Novak ve I. Cristea, “Composition in $EL$-hyperstructures”, Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 1, ss. 45–58, 2019.
ISNAD Novak, Michal - Cristea, Irina. “Composition in $EL$-Hyperstructures”. Hacettepe Journal of Mathematics and Statistics 48/1 (Şubat 2019), 45-58.
JAMA Novak M, Cristea I. Composition in $EL$-hyperstructures. Hacettepe Journal of Mathematics and Statistics. 2019;48:45–58.
MLA Novak, Michal ve Irina Cristea. “Composition in $EL$-Hyperstructures”. Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 1, 2019, ss. 45-58.
Vancouver Novak M, Cristea I. Composition in $EL$-hyperstructures. Hacettepe Journal of Mathematics and Statistics. 2019;48(1):45-58.