982: Kernel of Ring Homomorphism

<The previous article in this series | The table of contents of this series | The next article in this series>

definition of kernel of ring homomorphism

---

Topics

About: ring

---

The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Note

---

Starting Context

• The reader knows a definition of ring.

---

Target Context

• The reader will have a definition of kernel of ring homomorphism.

---

Orientation

There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

---

Main Body

---

1: Structured Description

Here is the rules of Structured Description.

Entities:
$R_1$: $\in \{\text{ the rings }\}$
$R_2$: $\in \{\text{ the rings }\}$
$f$: $:R_1\to R_2$, $\text{ the ring homomorphisms }$
$\ast Ker(f)$: $=f^{-1}(0)\subseteq R_1$
//

Conditions:
//

---

2: Note

Note that it is not "$f^{-1}(1)$".

---

References

<The previous article in this series | The table of contents of this series | The next article in this series>