Hi,
I would like to ask the following question:
I would like to find with SAGE in a quick way all finite lattices having a partial operation $x\cdot y$, defined for $x\geq y$, satisfying the following properties:
(a) $\forall x\geq y\geq z:\ x\cdot z \leq x\cdot y$ and $(x\cdot y)\cdot (x\cdot z) = y\cdot z$
(b) $\forall x\geq y, z:\ x\cdot (y \wedge z) = x\cdot y \wedge x\cdot z$
(c) $(x \vee y)\cdot y = x\cdot (x \wedge y) $
(d) $\forall x\geq y:\ y\leq x\cdot y$ and $(x\cdot y)\cdot y = x$
This is equivalent to having the structure of an MV algebra (see Prop. 44 on page 34 of https://pnp.mathematik.uni-stuttgart.de/iaz/iaz1/Rump/32-35.pdf)
Such lattices are always distributive.
I would be grateful for any help.
