Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

6 Issues per year


IMPACT FACTOR 2016: 0.346
5-year IMPACT FACTOR: 0.412

CiteScore 2016: 0.42

SCImago Journal Rank (SJR) 2016: 0.489
Source Normalized Impact per Paper (SNIP) 2016: 0.745

Mathematical Citation Quotient (MCQ) 2016: 0.24

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 66, Issue 2 (Apr 2016)

Issues

Combining boolean algebras and -groups in the variety generated by chang’s mv-algebra

A. Di Nola / A. R. Ferraioli / B. Gerla
Published Online: 2016-07-04 | DOI: https://doi.org/10.1515/ms-2015-0144

Abstract

In this paper we investigate a class of MV-algebras built up by fixing a Boolean algebra, one of its maximal ideals and an -group. We use such class to characterize, in the variety generated by all perfect MV-algebras, those MV-algebras which have their perfect skeleton as a quotient, giving an axiomatization of such a class and a representation theorem.

MSC 2010: Primary 06D35; Secondary 06F20

Keywords: MV-algebras; perfect MV-algebras; lattice-ordered abelian groups

Dedicated to Professor Anatolij Dvurečenskij on the occasion of his 65th birthday

(Communicated by Sylvia Pulmannová)

REFERENCES

  • [1]

    BELLUCE, L. P.: Semisimple algebras of infinite valued logic and bold fuzzy set theory, Canad. J. Math. 38 (1986), 1356–1379.Google Scholar

  • [2]

    BURRIS, S.—SANKAPPANAVAR, H. P.: A course in Universal Algebra. Grad. Texts in Math., Springer-Verlag, New York, 1981.Google Scholar

  • [3]

    BĚLOHLÁVEK, R.: On the regularity of MV-algebras and Wajesberg hoops, Algebra Universalis 44 (2000), 375–377.Google Scholar

  • [4]

    CIGNOLI, R.—D’OTTAVIANO, I. M.—MUNDICI, D.: Algebraic Foundations of Many-Valued Reasoning, Kluwer Academic Publishers, Dordrecht-Boston-London, 2000.Google Scholar

  • [5]

    DI NOLA, A.—LETTIERI, A.: Perfect MV-algebras are categorically equivalent to abelian l-groups, Studia Logica 53 (1994), 417–432.Web of ScienceGoogle Scholar

  • [6]

    DI NOLA, A.—LETTIERI, A.: Equational characterization of all varieties of MV-algebras, J. Algebra 221 (1999), 463–474.Google Scholar

  • [7]

    DI NOLA, A.—LEUSTEAN, I.: Łukasiewicz logic and MV-algebras. In: Handbook of Mathematical Fuzzy Logic, Vol. 1 (P. Cintula, P. Hájek, C. Noguera, eds.). Stud. Log. (Lond.), College Publications, London, 2011.Google Scholar

  • [8]

    SIKORSKI, R.: Boolean Algebras, Springer-Verlang, Berlin-Göttingen-Heidelberg, 1960.Google Scholar

About the article

Received: 2014-02-12

Accepted: 2014-09-22

Published Online: 2016-07-04

Published in Print: 2016-04-01


Citation Information: Mathematica Slovaca, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0144.

Export Citation

© 2016 Mathematical Institute Slovak Academy of Sciences. Copyright Clearance Center

Comments (0)

Please log in or register to comment.
Log in