On some properties of quasi-MV algebras and $$\sqrt{^{\prime}}$$ quasi-MV algebras. Part II

The present paper is a sequel to Paoli F, Ledda A, Giuntini R, Freytes H (On some properties of QMV algebras and $$\sqrt{^{\prime}}$$QMV algebras, submitted). We provide two representation results for quasi-MV algebras in terms of MV algebras enriched with additional structure; we investigate the lattices of subvarieties and subquasivarieties of quasi-MV algebras; we show that quasi-MV algebras, as well as cartesian and flat $$\sqrt{^{\prime}}$$ quasi-MV algebras, have the amalgamation property.

[1]  P. Aglianò,et al.  On subtractive varieties III: From ideals to congruences , 1997 .

[2]  Ivan Chajda Normally presented varieties , 1995 .

[3]  Paolo Lipparini n-Permutable varieties satisfy non trivial congruence identities , 1995 .

[4]  Francesco Paoli,et al.  MV-Algebras and Quantum Computation , 2006, Stud Logica.

[5]  D. Mundici,et al.  Algebraic Foundations of Many-Valued Reasoning , 1999 .

[6]  A. Ursini On subtractive varieties, I , 1994 .

[7]  R. McKenzie,et al.  Algebras, Lattices, Varieties , 1988 .

[8]  W. Blok,et al.  On the structure of hoops , 2000 .

[9]  Yuichi Komori Super-Łukasiewicz propositional logics , 1981, Nagoya Mathematical Journal.

[10]  G. Grätzer,et al.  A Note on the Implicational Class Generated by a Class of Structures , 1973, Canadian Mathematical Bulletin.

[11]  Francesco Paoli,et al.  On some properties of quasi-MV algebras and $sqrt{prime}$-MV algebras , 2009 .

[12]  Francesco Paoli,et al.  Expanding Quasi-MV Algebras by a Quantum Operator , 2007, Stud Logica.

[13]  A. Ursini,et al.  Ideals in universal algebras , 1984 .

[14]  Tomasz Kowalski,et al.  Splittings in the variety of residuated lattices , 2000 .

[15]  Nikolaos Galatos,et al.  Minimal varieties of residuated lattices , 2005 .

[16]  Ada Lettieri,et al.  Equational characterization of all varieties of MV-algebras , 1999 .

[17]  Antonino Salibra,et al.  Topological incompleteness and order incompleteness of the lambda calculus , 2003, TOCL.