Algebra I – autumn 2024 – Homework 2
1. Determine all elements of the transition monoid of the automaton
1
b
FF
a // 2
a
((
b
66 3
a
((
b

4
a
TT
b
hh
2. Decide whether
φ: (Z4, +) × (Z3, +) → (Z6, +), φ ([a]4, [b]3) = [3a2
+ 2b]6,
where a, b ∈ Z, defines a map correctly. If so, decide whether it is surjective and whether it is a
homomorphism of monoids.