Book example - HackMD

Book example === HackMD **Book Mode** turns lists of links into a book . 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 **Book Mode** in the top right sharing 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 . 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 **Book Mode** in the top right sharing 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)