Free Modal Pseudocomplemented De Morgan Algebras

Authors

  • Aldo V. Figallo Aldo V. Figallo, Nora Oliva, Instituto de Ciencias Básicas, Universidad Nacional de San Juan, (5400) San Juan, Argentina
  • Nora Oliva
  • Alicia Ziliani Alicia Ziliani, Instituto de Matemática, Universidad Nacional del Sur, (8000) Bahía Blanca, Argentina

DOI:

https://doi.org/10.18778/0138-0680.47.2.02

Keywords:

Pseudocomplemented De Morgan algebras, congruences, free algebras

Abstract

Modal pseudocomplemented De Morgan algebras (or mpM-algebras) were investigated in A. V. Figallo, N. Oliva, A. Ziliani, Modal pseudocomplemented De Morgan algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 53, 1 (2014), pp. 65–79, and they constitute a proper subvariety of the variety of pseudocomplemented De Morgan algebras satisfying xΛ(∼x)* = (∼(xΛ(∼x)*))* studied by H. Sankappanavar in 1987. In this paper the study of these algebras is continued. More precisely, new characterizations of mpM-congruences are shown. In particular, one of them is determined by taking into account an implication operation which is defined on these algebras as weak implication. In addition, the finite mpM-algebras were considered and a factorization theorem of them is given. Finally, the structure of the free finitely generated mpM-algebras is obtained and a formula to compute its cardinal number in terms of the number of the free generators is established. For characterization of the finitely-generated free De Morgan algebras, free Boole-De Morgan algebras and free De Morgan quasilattices see: [16, 17, 18].

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Published

2018-06-30

How to Cite

Figallo, A. V., Oliva, N., & Ziliani, A. (2018). Free Modal Pseudocomplemented De Morgan Algebras. Bulletin of the Section of Logic, 47(2), 89–106. https://doi.org/10.18778/0138-0680.47.2.02

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Research Article

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