%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[12pt,a4paper,oneside]{amsart}
\usepackage[a4paper]{geometry}
\geometry{hmargin=1.8cm,top=2cm,bottom=2.5cm}

\usepackage{mathptmx} % Times font
%\DeclareMathAlphabet{\mathcal}{OMS}{cmsy}{m}{n} % but do not change mathcal symbols

\setlength{\parindent}{0pt}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}

\title{
Exam for ``Algebraic Structures'' (6ALGS) 
\\ 
summer semester 2023/2024
}

\maketitle

\thispagestyle{empty}

\section*{Questions set no. 4}

\vskip 20pt

\textbf{1.} 

Define ideal of a ring, and homomorphism of rings. Illustrate these
notions by examples. What is a relationship between these two notions?

\vskip 20pt 

\textbf{2.}

Give an example of a group of prime order, having an element $x$ different 
from 1 and such that $x^2 = 1$.

\vskip 20pt

\textbf{3.}

Compute the automorphism group of $\mathbb Z / 4\mathbb Z$.


\end{document}
