Wolfram Demonstrations Project

This is a visualization of the algebraic ring

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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Direct Sum of Rings