Open AccessFree Modal Pseudocomplemented De Morgan Algebras
Author(s) -
Aldo V. Figallo,
Nora Oliva,
Alicia Ziliani
Publication year - 2018
Publication title -
bulletin of the section of logic
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.225
H-Index - 13
eISSN - 2449-836X
pISSN - 0138-0680
DOI - 10.18778/0138-0680.47.2.02
Subject(s) - subvariety , congruence relation , variety (cybernetics) , interior algebra , mathematics , pure mathematics , modal , free algebra , finitely generated abelian group , quadratic algebra , non associative algebra , algebra over a field , algebra representation , jordan algebra , chemistry , cellular algebra , statistics , polymer chemistry
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].