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$

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