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m-zeroid [2016/11/21 10:42]
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m-zeroid [2016/11/21 11:09] (current)
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====Basic results==== ====Basic results====
 +All subdirectly irreducible algebras are linearly ordered.
 +
 +The lattice is always bounded, with top element $0$.
 +
 +The bottom element $-0$ is the identity of $+$.
 +
 +The dual operation $x\cdot y=-(-y+-x)$ is the fusion of a commutative integral involutive semilinear residuated lattice. In fact, m-zeroids are precisely the duals of these residuated lattices, which are also known as involutive IMTL algebras.
====Properties==== ====Properties====
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====Subclasses==== ====Subclasses====
-[[]] +[[TBD]]
====Superclasses==== ====Superclasses====
-[[]]  +[[TBD]]
- +
-[[]]  +
- +
-[[]] +
====References==== ====References====
-[(PG1994> 
J. B. Palmatier and F. Guzman, J. B. Palmatier and F. Guzman,
\emph{M-zeroids structure and categorical equivalence}, \emph{M-zeroids structure and categorical equivalence},
Studia Logica, Studia Logica,
-\textbf{100}(5) 2012, 975--1000)] +\textbf{100}(5) 2012, 975--1000
- +
-[(COM2000> +
-Roberto L. O. Cignoli, Itala M. L. D'Ottaviano, Daniele Mundici, +
-\emph{Algebraic foundations of many-valued reasoning}, +
-Trends in Logic---Studia Logica Library +
-\textbf{7} Kluwer Academic Publishers +
-2000, x+231)] +
- +
-[(Mu1987> +
-Daniele Mundici, +
-\emph{Bounded commutative BCK-algebras have the amalgamation property}, +
-Math. Japon., +
-\textbf{32} 1987, 279--282)]+