Left Weak Distributivity

Nidus Idearum. Scilogs, IX: neutrosophia perennis

Similarly we get a neutrosophic triplet of the strong homomorphisms: (Strong-Homomorphism, NeutroStrong-Homomorphism, AntiStrong-Homomorphism.

They make perfect sense.

No matter what definition of hyper-homomorphism we use, we just apply the same Neutro-sophication and Anti-sophistication of the definition.

Left Weak Distributivity

Florentin Smarandache

The Left (Strong) Associativity and Left Weak Associativity apply to HyperAlgebras, where instead of equality ( = ), one uses non-empty intersection ( ∩ ).

Let U be a universe of discourse, a non-empty set X  U, and P(X) the power-set of X (all subsets of X, except the empty set ��).

A HyperAlgebra (X, *, #) with two well-defined binary operations:

while

2 * : ( ) X P X  and 2 # : ( ) X P X  , , ,x y z X  x*(y#z) = (x*y)#(x*z)

(left strong distributivity); (1)

, , ,x y z X  x*(y#z) ∩ (x*y)#(x*z) ≠ ��,

(left weak distributivity). (2) But these are totally different from NeutroAxiom, because both the Left Strong Distributivity and the Left Weak Distributivity are satisfied (are true) for all