At page 5, the stream ring is defined as a product of the coefficient ring and the function ring and from there, the notation gets heavy and there was little I could do. Hopefully by building confidence in the reader up to page 5, they would have the patience to forge ahead because the true nuggets of value are in the latter parts of the article.
Finally, to the "Captain" comment -- this article was written while in the Sea of Cortez aboard the S/V Red Herring: http://svredherring.com and https://twitter.com/SV_RedHerring.