(See Exercise 51.)
a. Write out the elements of
this ring. (Suggestion: Write
b. Is
c. Identify the unity elements, if one exists.
d. Find all units, if any exist.
e. Find all zero divisors, if any exist.
f. Find all idempotent elements, if any exist.
g. Find all nilpotent elements, if any exist.
Exercise 51.
Let
be arbitrary rings. In the Cartesian product
and
Prove that the Cartesian product is a ring with respect to these operations. It is called the direct sum of
Prove that
Prove
has a unity element if both
have unity elements.
Given as example of rings
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Chapter 5 Solutions
Elements Of Modern Algebra
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- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,