As usual, it is simpler to begin by looking at a more general setting—in this case, commutative rings—before getting involved with polynomial rings. It turns out that the nature of the ideals in a commutative ring is important: for example, we have already seen that gcd's exist in PIDs, while this may not be true in other commutative rings.

How do you do? began Pollyanna politely. I'm from Miss Polly Harrington, and I'd like to see Mrs. Snow, please.

Personal unions were scarcely new in British history. From 1066, England had been linked to parts of France under the Norman and then the Plantagenet dynasties. The accession of James VI to the English throne began a personal union that was not extended to a parliamentary union until 1707, while, under William III (1689-1702), the position of the house of Orange in Dutch politics was extended to Britain. Personal unions were also common on the Continent: for the eighteenth century, the list would include those of Poland and Saxony, Sweden and Hesse-Cassel, Russia and Holstein-Gottorp, and Denmark and Oldenburg.

In place of the humble but hopeful supplication of the Introibo, we have the narcissistic, desperate anguish of 1, punctuated by a blues refrain in the key of death and loss, drunkenness, violence, and sexuality.