Direct Sum of Rings

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This is a visualization of the algebraic ring .
Contributed by: Aaron Dunigan AtLee (March 2011)
Open content licensed under CC BY-NC-SA
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is represented as a circle with equally spaced integers from 0 to
. The two circles for
and
are combined to form a torus, representing the direct sum
. Elements of this ring are of the form
, where
and
. Thus
form coordinates of a point on the surface of the torus. The two-dimensional grid shows the unwrapped torus. Points A and B represent two elements of
and can be dragged in the lower grid to change their values. The sum and product of A and B are both shown.
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