Timeline for Nice examples of groups which are not obviously groups
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 10, 2014 at 19:01 | history | edited | Alexander Gruber♦ | CC BY-SA 3.0 | added 4 characters in body |
| Apr 17, 2013 at 16:57 | comment | added | Lubin | Although I was equally surprised when I saw this example, I became less surprised when I realized that it’s just the (completed) semigroup ring over $F$, where the semigroup in question is the set of positive integers under multiplication. If you use the set of nonnegative integers under addition, you get instead $F[[t]]$. | |
| Apr 16, 2013 at 20:32 | comment | added | anon | The ring can in fact be described in more familiar terms as $F[[x_2,x_3,x_5,x_7,\cdots]]$ (which can be thought of as the ring of formal Dirichlet series), where the formal variables are indexed by primes. The monomials $\prod x_{p_i}^{e_i}$ correspond to the indicator aka characteristic functions of the singleton sets $\{\prod p_i^{e_i}\}$. | |
| Apr 16, 2013 at 13:16 | history | edited | Alexander Gruber♦ | CC BY-SA 3.0 | deleted 2 characters in body |
| S Apr 16, 2013 at 12:40 | history | suggested | CommunityBot | CC BY-SA 3.0 | fix formula display |
| Apr 16, 2013 at 12:36 | review | Suggested edits | |||
| S Apr 16, 2013 at 12:40 | |||||
| Apr 15, 2013 at 20:10 | history | edited | Alexander Gruber♦ | CC BY-SA 3.0 | added 199 characters in body |
| Apr 15, 2013 at 18:28 | history | made wiki | Post Made Community Wiki by Qiaochu Yuan | ||
| Apr 15, 2013 at 15:47 | comment | added | Martin Brandenburg | Actually arithmetic functions constitute a ring (with pointwise addition, and Dirichlet convolution as multiplication). Here, $f$ is a unit iff $f(1) \neq 0$ (you should add this to your answer). This is also quite similar (replacing $|$ by $\leq$) to the classification of units in rings of formal power series; only the constant term has to be invertible. | |
| Apr 15, 2013 at 15:37 | history | edited | Alexander Gruber♦ | CC BY-SA 3.0 | edited body |
| Apr 15, 2013 at 15:09 | history | answered | Alexander Gruber♦ | CC BY-SA 3.0 |