Sunday, March 20, 2005

Object Ring

The object ring is defined by two conditions, and includes all numbers such that these conditions are true:

1. 1 and -1 are the only rationals that are units in the ring.

2. Given a member m of the ring there must exist a non-zero member n such that mn is an integer, and if mn is not a factor of m, then n cannot be a unit in the ring.

1 comment:

Anonymous said...

What set are numbers pulled from? The set of reals? The set of complex numbers? Something else? You don't say, but the tone seems to be that the elements of the object ring are from the complex numbers.

Why did you choose these conditions? Did you make them up yourself? Did you find them from a book or journal article?

If you made them up yourself, why? That is, why these two particular conditions? What is to be gained by defining such a 'ring'?

If you got them from another source, please cite it.