Division ring
In abstract algebra, a division ring, also called a skew field, is a ring with 0 ≠ 1 and such that every non-zero element a has a multiplicative inverse (i.e. an element x with ax = xa = 1). Division rings are very similar to fields except that their multiplication isn't required to be commutative. The condition 0 ≠ 1 is only there to exclude the trivial ring with a single element 0 = 1.All fields are division rings. A more typical example is given by the quaternions. If we allow only rational instead of real coefficients in the constructions of the quaternions, we obtain another division ring. In general, if R is a ring and S is a simple module over R, then the endomorphism ring of S is a division ring; every division ring arises in this fashion from some simple module.
All of linear algebra may be formulated, and remains correct, for modules over division rings instead of vector spaces over fields. Every module over a division ring has a basis; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gauss-Jordan elimination algorithm remains applicable.
All finite division rings are commutative and therefore finite fields.
See also: division, division algebra
mainland--that is all. It is the price of your lives. Do you agree?"
Sullenly the Wieroos acquiesced. Bradley examined the knots that
the girl.html">girl.html">girl to mount the back of the leading Wieroo, himself upon
With loud flapping of the powerful wings the creatures took to
and then taking a course due west out over the waters of the sea.
Nowhere about them could Bradley see signs of other Wieroos, nor
to his plans for escape--the huge, winged reptilia that are so
seen, though in lesser numbers, farther north.
Nearer and nearer loomed the mainland--a broad, parklike expanse
The little dots in the foreground became grazing herds of deer
mudhole to the right, and beyond, a mighty mammoth culled the
of giant carnivora came faintly to their ears. Ah, this was Caspak.
fullness to the throat of the Englishman as to one who sees and
Then the Wieroos dropped swiftly downward to the flower-starred
from their backs, and Bradley told the red-robed creatures they
uncanny wailing upon their lips that always brought a shudder to
frightful Oo-oh.
When the creatures had gone, the girl turned toward Bradley.
far from my country. We may never live to reach it, as we are
surely as would the Wieroos should they capture us, and we have
there are two Wieroo cities at the eastern end of the island.
about our heads hundreds of the creatures from whom we could not
it cannot be over two marches to the fort of which I have told you.
a way to return you to your people."
"And you?" asked the girl.
"I escaped from Oo-oh," replied Bradley. "I have accomplished
.
On
wordlookup.net
All is still licensed under the GNU FDL.
It uses material from the wikipedia.
|
|