On Ternary Monoid of All Hypersubstitutions of Type \(\tau=(2)\)

Nagornchat Chansuriya, Sorasak Leeratanavalee


The present paper gives the concept of a ternary monoid \(\mathit{Hyp}(2)\) and studies some algebraic-structural properties of this monoid. We consider some submonoids of \(\mathit{Hyp}(2)\) and study the relationship between these submonoids.


Hypersubstitutions; Ternary semigroup; Ternary ideal

Full Text:



K. Denecke and J. Koppitz, Finite monoid of hypersubstitutions of type (tau=(2)), Semigroup Forum 56 (1998), 265 – 275, DOI: 10.1007/PL00005945.

K. Denecke and Sh. L. Wismath, The monoid of hypersubstitutions of type (tau=(2)), Contributions to General Algebra, Klagenfurt 10 (1998), 109 – 127.

W. A. Dudek, Idempotents in n-ary semigroups, Southeast Asian Bull. Math. 25 (2001), 97 – 104, DOI: 10.1007/s10012-001-0097-y.

W. A. Dudek and I. Groúdzinska, On ideals in regular n-semigroups, Mat. Bilten (Skopje) 4(XXX) (1980), 35 – 44.

J. M. Howie, An Introduction to Semigroup Theory, Academic Press Inc., London (1976).

A. Iampan, Some properties of ideal extensions in ternary semigroups, Iranian Journal of Mathematical Sciences and Informatics 8(1) (2013), 67 – 74, DOI: 10.7508/ijmsi.2013.01.007.

S. Kar and B. K. Maity, Congruences on ternary semigroups, Journal of Chungcheong Mathematical Society 20(3) (2007), 191 – 201.

E. Kasner, An extension of the group concept, (reported by Weld L. G.), Bull. Amer. Math. Soc. 10 (1904), 290 – 291.

J. Koppitz and K. Denecke, M-Solid Varieties of Algebras, Springer Science+Business Media, Inc., New York (2006), DOI: 10.1007/0-387-30806-7.

M. L. Santiago and S. Sri Bala, S Ternary semigroups, Semigroup Forum 81 (2010), 380 – 388, DOI: 10.1007/s00233-010-9254-x.

Y. Sarala, A. Anjaneyulu and D. Madhusudhana Rao, Pseudo symmetric ideals in ternary semigroups, International Refereed Journal of Engineering and Science (IRJES) 1(4) (2012), 33 – 43.

F. M. Siosan, Ideals in ((m +1))-semigroups, Ann. Mat. Pura Appl. 68 (1965), 161 – 200, DOI: 10.1007/BF02411024.

F. M. Siosan, Ideal theory in ternary semigroups, Math. Japan. 10 (1965), 63 – 84.

F. M. Siosan, On regular algebraic systems: A note on notes by Iseki, Kovacs, and Lajos, Proc. Japan. Acad. 39 (1963), 283 – 286, DOI: 10.3792/pja/1195523057.

DOI: http://dx.doi.org/10.26713%2Fcma.v10i4.1256


  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905