Strongly Solid Varieties in Many-Sorted Algebras

Authors

  • Dawan Chumpungam Ph.D. Degree Program in Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200
  • Sorasak Leeratanavalee Center of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200

DOI:

https://doi.org/10.26713/cma.v9i4.972

Keywords:

many-sorted algebra, i-sorted $\Sigma$-generalized hypersubstitution, i-sorted $\Sigma$-algebras, $\Sigma$-terms, $\Sigma_identity$

Abstract

In this paper, we apply the general theory of conjugate pairs of additive closure operators to characterize the strongly solid variety which is extended from one-sorted algebras to many-sorted algebras. Moreover, we give the concept of \(V\)-normal form which is useful for testing the strongly solid variety in many-sorted algebra.

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References

G. Birkhoff and J.D. Lipson, Heterogeneous algebras, J. Combin. Theory 8 (1970), 115 – 133.

K. Denecke and S. Lekkoksung, Hyperidentities in many-sorted algebras, Discussiones Mathematicae General Algebra and Applications 29 (2009) 47 – 74.

K. Denecke and S. Lekkoksung, Hypersubstitutions of many-sorted algebras, Asian-Eur. J. Math. 1(3) (2008), 337 – 346, DOI: 10.1142/S179355710800028X.

S. Leeratanavalee and K. Denecke, Generalized Hypersubstitutions and Strongly Solid Varieties, General Algebra and Applications, Proc. of the 59 th Workshop on General Algebra, 15-th Conference for Young Algebraists Potsdam 2000, Shaker Verlag (2000).

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Published

25-12-2018
CITATION

How to Cite

Chumpungam, D., & Leeratanavalee, S. (2018). Strongly Solid Varieties in Many-Sorted Algebras. Communications in Mathematics and Applications, 9(4), 677–688. https://doi.org/10.26713/cma.v9i4.972

Issue

Vol. 9 No. 4 (2018)

Section

Research Article

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