Research article

Clones of inductive superpositions of terms

  • Received: 22 September 2022 Revised: 27 December 2022 Accepted: 12 January 2023 Published: 18 January 2023
  • MSC : 08A35, 08A40, 08A70, 08B20

  • A superposition is an operation of terms by which we substitute each variable within a term with other forms of terms. With more options of terms to be replaced, an inductive superposition is apparently more general than the superposition. This comes with a downside that it does not satisfy the superassociative property on the set of all terms of a given type while the superposition does. A derived base set of terms on which the inductive superposition is superassociative is given in this paper. A clone-like algebraic structure involving such base set and superposition is the main topic of this paper. Generating systems of the clone-like algebra are characterized and it turns out that the algebra is only free with respect to itself under the certain selections of fixed terms concerning its inductive superposition or the specific type of its base set.

    Citation: Pongsakorn Kitpratyakul, Bundit Pibaljommee. Clones of inductive superpositions of terms[J]. AIMS Mathematics, 2023, 8(4): 7747-7765. doi: 10.3934/math.2023389

    Related Papers:

  • A superposition is an operation of terms by which we substitute each variable within a term with other forms of terms. With more options of terms to be replaced, an inductive superposition is apparently more general than the superposition. This comes with a downside that it does not satisfy the superassociative property on the set of all terms of a given type while the superposition does. A derived base set of terms on which the inductive superposition is superassociative is given in this paper. A clone-like algebraic structure involving such base set and superposition is the main topic of this paper. Generating systems of the clone-like algebra are characterized and it turns out that the algebra is only free with respect to itself under the certain selections of fixed terms concerning its inductive superposition or the specific type of its base set.



    加载中


    [1] S. Burris, H. Sankappanavar, A course in universal algebra, New York: Springer, 2012.
    [2] K. Denecke, Strongly solid varieties and free generalized clones, Kyungpook Math. J., 45 (2005), 33–43.
    [3] K. Denecke, The partial clone of linear terms, Sib. Math. J., 57 (2016), 589–598. https://doi.org/10.1134/S0037446616040030 doi: 10.1134/S0037446616040030
    [4] K. Denecke, H. Hounnon, Partial Menger algebras of terms, Asian-Eur. J. Math., 14 (2021), 2150092. https://doi.org/10.1142/S1793557121500923 doi: 10.1142/S1793557121500923
    [5] K. Denecke, P. Jampachon, Clones of full terms, Algebra Discret. Math., 4 (2004), 1–11.
    [6] K. Denecke, S. Leeratanavalee, Kernels of generalized hypersubstitutions, Proceedings of Sixth International Conference on Discrete Mathematics and Applications, 2001, 87–96.
    [7] K. Denecke, S. Wismath, Hyperidentities and clones, London: Gordon and Breach Science Publishers, 2000. https://doi.org/10.1201/9781482287516
    [8] K. Denecke, S. Wismath, Universal algebra and applications in theoretical computer science, Boca Raton: Chapman & Hall/CRC, 2002.
    [9] F. Gécseg, M. Steinby, Tree automata, Budapest: Akadémiai Kiadó, 1984.
    [10] P. Kitpratyakul, B. Pibaljommee, On substructures of semigroups of inductive terms, AIMS Mathematics, 7 (2022), 9835–9845. https://doi.org/10.3934/math.2022548 doi: 10.3934/math.2022548
    [11] P. Kitpratyakul, B. Pibaljommee, Semigroups of an inductive composition of terms, Asian-Eur. J. Math., 15 (2022), 2250038. https://doi.org/10.1142/S1793557122500383 doi: 10.1142/S1793557122500383
    [12] J. Koppitz, K. Denecke, M-solid varieties of algebras, New York: Springer, 2006. https://doi.org/10.1007/0-387-30806-7
    [13] N. Lekkoksung, S. Lekkoksung, On partial clones of $k$-terms, Discussiones Mathematicae-General Algebra and Applications, 41 (2021), 361–379. https://doi.org/10.7151/dmgaa.1367 doi: 10.7151/dmgaa.1367
    [14] B. Schein, V. Trokhimenko, Algebras of multiplace functions, Semigroup Forum, 17 (1979), 1–64. https://doi.org/10.1007/BF02194309 doi: 10.1007/BF02194309
    [15] Sl. Shtrakov, Composition of terms and essential positions in deduction, 2008, arXiv: 0802.2385v1.
    [16] Sl. Shtrakov, Multi-solid varieties and mh-transducers, Algebra Discret. Math., 3 (2007), 113–131.
    [17] K. Wattanatripop, T. Changphas, Clones of terms of a fixed variable, Mathematics, 8 (2020), 260. https://doi.org/10.3390/math8020260 doi: 10.3390/math8020260
    [18] K. Wattanatripop, T. Changphas, The length of terms and their measurement, International Journal of Mathematics andComputer Science, 16 (2021), 1103-–1116.
  • Reader Comments
  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1323) PDF downloads(149) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog