Commutative Algebra: Primary decomposition 1 - Oxford Mathematics 3rd Year Student Lecture

In this lecture, one of two we are showing from Dawid Kielak's 3rd year course on Commutative Algebra, we demonstrate that every integer is a product of powers of primes, and every polynomial in a single variable over a field is a product of powers of irreducible polynomials. How far does this generalise over arbitrary commutative rings? You can watch the second lecture here: https://youtu.be/uKlQ-11iwHA You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE All first and second year lectures are followed by tutorials where students meet their tutor in pairs to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.