---
# System prepended metadata

title: Book example

---

Book example
===
HackMD **Book Mode** turns lists of links into a book <i class="fa fa-book"></i>.
You could group links under header tags and create chapter-like sections. [Learn more here](https://hackmd.io/c/tutorials/%2Fs%2Fhow-to-create-book).
Choose <i class="fa fa-book"></i> **Book Mode** in the top right sharing <i class="fa fa-share-alt fa-18"></i> menu and hit "**Preview**" to see your book.
:::info
:bulb: **Hint:** In book mode, only list of links and headings will appear in the left-hand bar.
:::

Documentation
---
- [Features](/s/features)
- [YAML Metadata](/yaml-metadata)
- ### Publish mode
  - [Slide example](/p/slide-example)
  - [Book example](/book-example)
  - [Release notes](/s/release-notes)

Information
---
- [Terms](/s/terms)
- [Privacy](/s/privacy)

External Link
---
You could also add `[target=_blank]` to force the link open in new tab, like this:
- [Release Notes](/s/release-notes) [target=_blank]

**If you add a link starts with http (non-SSL), we'll also make it open in new tab.**

Closed List [close]
---

You could add `[close]` to heading to make sure the list is closed by default.

- [Link 1](/s/release-notes)
- [Link 2](/s/release-notes)
- [Link 3](/s/release-notes)







# ***A Survey of Modern Algebra***

## Chapter 1: The Integers


#### 1.1 Commutative Rings; Integral Domains

> Defintion. Let *R* be a set of elements *a, b, c, ...* for which the sum *a + b* and the product *ab* of any two elements *a* and *b* (distinct or not) of *R* are defined. Then *R* is called a **commutative ring**  if the following postulates (i) - (viii) hold:

(i) *Closure*. If $a$ and $b$ are in $R$, then the sum $a + b$ and the product $ab$ are in $R$.
(ii) *Uniqueness*. If $a$ = $a'$ and $b$ = $b'$ in $R$, then $a + b = a' + b'$ and $ab = a'b'$. 
(iii) *Commutative laws*. For all $a$ and $b$ in $R$, $a + b = b + a$, $ab = ba$.
(iv) 


> Definition. An integral domain is a *commutative ring* in which the following additional postulate holds:

(ix) *Cancellation law*. If $c \neq 0$ and $ca = cb$, then $a = b$.


#### 1.2 Elementary Properties of Commutative Rings
Three basic laws for equality:
1. **Reflexive law**: $a=a$.
2. **Symmetric law**: If $a=b$, then $b=a$.
3. **Transitive law**: If $a=b$ and  $a=c$, then $a=c$ , valid for all $a$, $b$ and $c$.

***RULE 1***.  $(a+b)c = ac +bc$, for all $a$, $b$ and $c$ in $R$.













Book example
===

HackMD **Book Mode** turns lists of links into a book <i class="fa fa-book"></i>.
You could group links under header tags and create chapter-like sections. [Learn more here](https://hackmd.io/c/tutorials/%2Fs%2Fhow-to-create-book).
Choose <i class="fa fa-book"></i> **Book Mode** in the top right sharing <i class="fa fa-share-alt fa-18"></i> menu and hit "**Preview**" to see your book.
:::info
:bulb: **Hint:** In book mode, only list of links and headings will appear in the left-hand bar.
:::

Documentation
---
- [Features](/s/features)
- [YAML Metadata](/yaml-metadata)
- ### Publish mode
  - [Slide example](/p/slide-example)
  - [Book example](/book-example)
  - [Release notes](/s/release-notes)

Information
---
- [Terms](/s/terms)
- [Privacy](/s/privacy)

External Link
---
You could also add `[target=_blank]` to force the link open in new tab, like this:
- [Release Notes](/s/release-notes) [target=_blank]

**If you add a link starts with http (non-SSL), we'll also make it open in new tab.**

Closed List [close]
---

You could add `[close]` to heading to make sure the list is closed by default.

- [Link 1](/s/release-notes)
- [Link 2](/s/release-notes)
- [Link 3](/s/release-notes)
