Free Modal Pseudocomplemented De Morgan Algebras

Aldo V. Figallo; Nora Oliva; Alicia Ziliani

Bulletin of the Section of Logic (2018)

  • Volume: 47, Issue: 2
  • ISSN: 0138-0680

Abstract

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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].

How to cite

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Aldo V. Figallo, Nora Oliva, and Alicia Ziliani. "Free Modal Pseudocomplemented De Morgan Algebras." Bulletin of the Section of Logic 47.2 (2018): null. <http://eudml.org/doc/295580>.

@article{AldoV2018,
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].},
author = {Aldo V. Figallo, Nora Oliva, Alicia Ziliani},
journal = {Bulletin of the Section of Logic},
keywords = {Pseudocomplemented De Morgan algebras; congruences; free algebras},
language = {eng},
number = {2},
pages = {null},
title = {Free Modal Pseudocomplemented De Morgan Algebras},
url = {http://eudml.org/doc/295580},
volume = {47},
year = {2018},
}

TY - JOUR
AU - Aldo V. Figallo
AU - Nora Oliva
AU - Alicia Ziliani
TI - Free Modal Pseudocomplemented De Morgan Algebras
JO - Bulletin of the Section of Logic
PY - 2018
VL - 47
IS - 2
SP - null
AB - 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].
LA - eng
KW - Pseudocomplemented De Morgan algebras; congruences; free algebras
UR - http://eudml.org/doc/295580
ER -

References

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