Table of Contents
Generalized MV-algebras
Abbreviation: GMV
Definition
A generalized MV-algebra is a residuated lattices $\mathbf{L}=\langle L,\vee, \wedge, \cdot, e, \backslash, /\rangle$ such that
$x\vee y=x/(y\backslash x\wedge e)$, $x\vee y=(x/y\wedge e)\backslash y$
Morphisms
Let $\mathbf{L}$ and $\mathbf{M}$ be generalized MV-algebras. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a homomorphism:
$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$, $h(x\backslash y)=h(x)\backslash h(y)$, $h(x/y)=h(x)/h(y)$, $h(e)=e$
Examples
Example 1:
Basic results
Properties
Finite members
$\begin{array}{lr} f(1)= &1\\ f(2)= &1\\ f(3)= &\\ f(4)= &\\ f(5)= &\\ f(6)= &\\ \end{array}$
Subclasses
Superclasses
References
Trace: » generalized_mv-algebras