# Quantized Space: General Form

1. Jan 9, 2004

### Antonio Lao

For n by n matrices

$$H^{+}_n$$

$$H^{-}_n$$

a(Hn+)(bHn-)=n^(m-1)Hn+, if a and b are even integers,

a(Hn+)(bHn-)=n^(m-1)Hn-, if a and b are odd integers, where m=a+b.

H+, H- and H0, using traditional concepts from abstract algebras, form a ring that is an abelian group under addition and a semigroup under multiplication with a commutative binary operation and integer scalar multiplication factors that are integer power expressions.

The following rules can be applied for the grouping of space charges:

1. Only space charges of the same order can interact.
2. Each LOE can have maximum 8 space charges.
3. Only space charges of the same order are allow in each LOE.
4. Only space charges within LOE are allowed to interact
5. One level of LOE can become next order of space charges for
the next higher level of LOE so on and so forth.