# A Very Short Introduction to Regular Sequences

Take yourself away from this cold day in December and transport yourself to the world of commutative rings with identity. In this land there is a wonderful tool called the theory of regular sequences, which we will examine in this post. Our aim will be to get a quick idea of what regular sequences are, without going into too much tedious detail, with the hope that everyone reading this will think regular sequences are cool.

Now before I even define regular sequences, let us look at some examples of regular sequences:

1. In the ring $k[x,y,z]$, the sequence $x,y,z$.
2. In the ring $\mathbb{Z}[x]$, the sequence $2,x$.
3. In the ring $\mathbb{Z}$, the sequence $4$