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By Poul Anderson

A terrific story of intrigue, love, warfare, magic, and swashbuckling experience set in another universe the place fairies mingle freely with Englishmen and all of Shakespeare's fictional characters are real

Welcome to another civil-war-torn seventeenth-century England—a international the place Hamlet as soon as brooded and Othello jealously raged. right here faeries and sprites gambol in English woods, railroads race around the panorama whereas manned balloons go with the flow above the geographical region, and the main revered historian of all is one William Shakespeare of Stratford-upon-Avon.

The yr is 1644, and the battle among the Roundheads and the Cavaliers rages. while Rupert, nephew of King Charles I, is taken captive by way of Cromwell's troops and imprisoned in a Puritan domestic, he's instantly smitten with the attractive Jennifer Alayne, his captor's niece. Escaping with the aid of his newfound liked and the unswerving trooper Will Fairweather, Rupert leads Jennifer deep into the woodland, the place the faerie people who reside there have a vested curiosity within the end result of the good and bloody clash. although the fanatics needs to quickly part—with the prince venture a perilous venture for his magical benefactors which may flip the tide of war—Rupert and his girl love could be perpetually joined via the earrings provided to them through King Oberon and Queen Titania. And regardless of the unusual, twisting pathways and turbulent seas they're destined to come across, they're going to constantly be capable to locate one another again... so long as their love continues to be true.

Nominated for the realm fable Award and winner of the Mythopoeic Award, Poul Anderson's A Midsummer Tempest is a massive achievement—a pleasant alternate-history delusion that brings the fictitious worlds of Shakespeare's performs to breathtaking existence with sort, wit, and unprecedented mind's eye.

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Extra resources for A Midsummer Tempest (Operation Otherworld, Book 3)

Example text

Sometimes there is also an injection g : S → R such that f ◦g is the identity function (a right inverse of f ). In this case it makes sense to think of S as a subring of R so that R is an algebra over S. We say that g is a splitting of f . If R is a ring and a ∈ R, then the annihilator Za of a is an ideal. It is proper because 1 ∈ Za . c Characteristic Let R be a commutative ring. If m is a nonnegative integer, we write m ∈ R for the sum 1+1 · · ·+1 (m times). This defines a homomorphism from Z into R.

3) This follows from (1) and (2). For example, consider the ring of ordinary integers Z. Let I be an ideal containing a nonzero element. Multiplication by −1 preserves membership in I, so I contains a positive element. Let m be the least positive element of I. Suppose that a ∈ I is any other element of I. Then gcd(m, a) = um + va for some integers u and v, so gcd(m, a) ∈ I. We have gcd(m, a) ≤ m, so by the minimality of m, gcd(m, a) = m. That is, m divides a. Since every multiple of m is in I, it follows that I consists exactly of the multiples of m.

3. If R is a field then R[x] is a Euclidean domain with δ(f ) = deg(f ). 4. If a is a root of f (x) ∈ R[x], then there exists a polynomial q(x) ∈ R[x] such that f (x) = (x − a)q(x). If R is an integral domain, then the number of distinct roots of f is no more than the degree of f (but see exercise 16). Proof. 2) with g = x − a. The remainder r has degree zero but has a as a root. Thus r is zero. If R is an integral domain and if b = a is another root of f (x) then b is necessarily a root of q(x).

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