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Congruence Pairs of Decomposable MS-Algebras

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Abstract

In this paper, the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras (see [13]). They show that every congruence relation θ on a decomposable MS-algebra L can be uniquely determined by a congruence pair (θ1,θ2), where θ1 is a congruence on the de Morgan subalgebra L°° of L and θ2 is a lattice congruence on the sublattice D(L) of L. They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L. Moreover, they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.

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Acknowledgement

The authors would like to thank the editors and referees for their valuable comments and suggestions to improve this presentation.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

    Sanaa El-Assar & Abd El-Mohsen Badawy

Authors
  1. Sanaa El-Assar
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  2. Abd El-Mohsen Badawy
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Corresponding authors

Correspondence to Sanaa El-Assar or Abd El-Mohsen Badawy.

Additional information

*This work was supported by 2nd International Conference for Mathematics, Statistics and Information Technology (ICMSIT for short) that held in the Faculty of Science, Tanta University, Egypt, 18–20 December, 2018.

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El-Assar, S., Badawy, A.EM. Congruence Pairs of Decomposable MS-Algebras. Chin. Ann. Math. Ser. B 42, 561–574 (2021). https://doi.org/10.1007/s11401-021-0278-1

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  • DOI: https://doi.org/10.1007/s11401-021-0278-1

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