DM-GAA

Article in press

Authors:

T. Kumduang

Thodsaporn Kumduang

Department of Mathematics
Faculty of Science and Technology
Rajamangala University of Technology Rattanakosin
Nakhon Pathom 73170, Thailand

email: kumduang01@gmail.com

K. Wattanatripop

Khwancheewa Wattanatripop

Department of Mathematics
Faculty of Science and Agricultural Technology
Rajamangala University of Technology Lanna
Chiang Mai 50300, Thailand

email: khwancheewa.wat@rmutl.ac.th

T. Changphas

Thawhat Changphas

email: thacha@kku.ac.th

Title:

Algebras of full terms constructed from transformations with fixed set

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2022-08-03 , Revised: 2022-11-26 , Accepted: 2022-11-27 , Available online: 2024-02-08 , https://doi.org/10.7151/dmgaa.1451

Abstract:

Based on th notion of full transformations with fixed set, in this paper, we present a novel concept of $n$-ary $Fix(I_n,Y)$-full terms. This term can be considered as a generalization of strongly full terms, permutational full terms and full terms. Together with the superposition operation, one can form a Menger algebra of rank $n$. The freeness of such algebra with respect to a variety of algebras of the same types is discussed. Furthermore, we apply hypersubstitution theory to define a $Fix(I_n,Y)$-full closed identity, a $Fix(I_n,Y)$-full closed variety and present some concrete examples.

Keywords:

transformations with fixed set, full term, Menger algebra, hypersubstitution

References:

T. Changphas and K. Denecke, Green's relations on the seminearring of full hypersubstitutions of type $(n)$, Algebra Discrete Math. 2 (2003) 6–19.
K. Denecke, The partial clone of linear terms, Sib. Math J. 57(4) (2016) 589–598.
https://doi.org/10.1134/S0037446616040030
K. Denecke and H. Hounnon, Partial Menger algebras of terms, Asian-Eur. J. Math. 14(6) (2021) 2150092.
https://doi.org/10.1142/S1793557121500923
K. Denecke and L. Freiberg, The algebra of strongly full terms, Novi Sad J. Math. 34 (2004) 87–98.
K. Denecke and P. Jampachon, Clones of full terms, Algebra and Discrete Math. 4 (2004) 1–11.
K. Denecke and S.L. Wismath, Hyperidentities and Clones (Gordon and Breach Science Publishers, 2000).
https://doi.org/10.1201/9781482287516
W.A. Dudek and V.S. Trohimenko, Algebras of Multiplace Functions (De Gruyter, Berlin, 2012).
https://doi.org/10.1515/9783110269307
W.A. Dudek and V.S. Trokhimenko, Menger algebras of associative and self-distributive $n$-ary operations, Quasigroups Relat. Syst. 26 (2018) 45–52.
E. Graczynska and D. Schweigert, Hypervarieties of a given type, Algebra Univ. 27 (1990) 305–318.
https://doi.org/10.1007/BF01190711
Y. Guellouma and H. Cherroun, From tree automata to rational tree expressions, Int. J. Found. Comput. Sci. 29(6) (2018) 1045–1062.
https://doi.org/10.1142/S012905411850020X
P. Honyam and J. Sanwong, Semigroups of transformations with fixed sets, Quaest Math. 36 (2013) 79–92.
https://doi.org/10.2989/16073606.2013.779958
P. Kitpratyakul and B. Pibaljommee, Semigroups of an inductive composition of terms, Asian-Eur. J. Math. 15(2) (2022) 2250038.
https://doi.org/10.1142/S1793557122500383
J. Koppitz and K. Denecke, M-Solid Varieties of Algebras (Springer, 2006).
T. Kumduang and S. Leeratanavalee, Left translations and isomorphism theorems of Menger algebras, Kyungpook Math. J. 61(2) (2021) 223–237.
https://doi.org/10.5666/KMJ.2021.61.2.223
S. Leeratanavalee, Submonoids of generalized hypersubstitutions, Demonstr. Math. 40 (2007) 13–22.
https://doi.org/10.1515/dema-2007-0103
N. Lekkoksung and S. Lekkoksung, On partial clones of $k$-terms, Discuss. Math. Gen. Algebra Appl. 41 (2021) 361–379.
https://doi.org/10.7151/dmgaa.1376
A. Nongmanee and S. Leeratanavalee, v-regular ternary Menger algebras and left translations of ternary Menger algebras, Mathematics 9(21) (2021) 2691.
https://doi.org/10.3390/math9212691
S. Phuapong and T. Kumduang, Menger algebras of terms induced by transformations with restricted range, Quasigroups Relat. Syst. 29 (2021) 255–268.
S. Phuapong and S. Leeratanavalee, The algebra of generalized full terms, Int. J. Open Problems Compt. Math. 4 (2011) 54–65.
S. Phuapong and C. Pookpienlert, $S(\bar{n_i},Y_i)$-terms and their algebraic properties, Thai J. Math. 20(1) (2021) 337–346.
K. Wattanatripop and T. Changphas, The clone of $K^*(n, r)$-full terms, Discuss. Math. Gen. Algebra Appl. 39(2) (2019) 277–288.
https://doi.org/10.7151/dmgaa.1319
K. Wattanatripop and T. Changphas, The Menger algebra of terms induced by order-decreasing transformations, Commun. Algebra. 49(7) (2021) 3114–3123.
https://doi.org/10.1080/00927872.2021.1888385