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{{\Large\bf MODERN ALGEBRA I}\\
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{\Large\bf HOMEWORK ASSIGNMENT V}\\
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{\bf (Turn in underlined problems.)}}
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{\bf 
\begin{tabbing}
\underline{\large\bf CHAPTER}\makebox[2in]{}\=\underline{\large\bf PROBLEMS}\\

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\noindent
1 \> 2.2, 2.3, \underline{2.5}, \underline{3.3},
\underline{3.10}, \underline{3.13}
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}
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\noindent
\underline{\large\bf ADDITIONAL PROBLEMS}
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{\bf 

\underline{1.} Let {\bf R} be a ring.
Show that if the sequence
$\langle 1, 1+1, 1+1+1, \ldots\rangle$
does not contain zero, then the ring elements
$1, 1+1, 1+1+1,\ldots$ are distinct from one another.

\bigskip

2. If {\bf R} is a ring, and there is a 
positive integer $n$ such that 
\[\underbrace{1+1+\cdots +1}_{n \;1'{\rm s}} = 0,\]
then the smallest such $n$ is called the
{\it characteristic} of {\bf R}. If there
is no such $n$, then the characteristic of {\bf R}
is zero.
Give an example of a ring whose characteristic
is not zero.

}
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