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Galois Theory, 4th Edition
book

Galois Theory, 4th Edition

by Ian Nicholas Stewart
March 2015
Intermediate to advanced content levelIntermediate to advanced
344 pages
10h 18m
English
Chapman and Hall/CRC
Content preview from Galois Theory, 4th Edition
186 Abstract Rings and Fields
Since I + 1 is the identity element of Z/I, we have found a multiplicative inverse for
the given element I + r. Thus every non-zero element of Z/I has an inverse, so that
Z
n
= Z/I is a field.
From now on, when dealing with Z
n
, we revert to the usual convention and write
the elements as 0,1,2,...,n 1 rather than I,I + 1,I + 2,...,I + n 1.
16.3 Polynomials Over General Rings
We now introduce polynomials with coefficients in a given ring. The main point
to bear in mind is that identifying polynomials with functions, as we cheerfully did
in Chapter 2 for coefficients in C, is no longer a good idea, because Proposition 2.3,
which ...
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Publisher Resources

ISBN: 9781482245837