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I know this is a soft question of sorts but I am curious why we can't just say "1" instead of "unity," e.g. a root of unity.

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    $\begingroup$ ... the concept extends to any algebraic unital ring. $\endgroup$ – oldrinb Apr 2 '13 at 21:41
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    $\begingroup$ @AsalBeagDubh out of curiosity did you manage to read past the first two paragraphs? "Unfortunately, the term unit is also used to refer to the identity element $1_R$ of the ring, in expressions like ring with a unit or unit ring, and also e.g. 'unit' matrix. (For this reason, some authors call $1_R$ "unity" or "identity", and say that $R$ is a "ring with unity" or a "ring with identity" rather than a "ring with a unit".)" $\endgroup$ – oldrinb Apr 2 '13 at 21:48
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    $\begingroup$ @oldrinb: Well, I read your second comment as saying that in a unital ring, the word unit only means multiplicative identity. In any case, I think this proves that the term "unity" is confusing! $\endgroup$ – user64687 Apr 2 '13 at 21:51
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    $\begingroup$ And, for those folks who are comfortable writing "ring with $1$" for "ring with unit(y)", why not also write "$0$-divisor" vs. "zero-divisor"? $\endgroup$ – Math Gems Apr 2 '13 at 21:55
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    $\begingroup$ @oldrinb: I get your meaning now! My two cents: I think people prefer "unity" because saying "a ring with one" sounds incomplete: the instinctive response is, "a ring with one what?" $\endgroup$ – user64687 Apr 2 '13 at 21:56
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We can.${}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}$

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    $\begingroup$ How did you avoid the "Body must be at least 30 characters; you entered 7."? $\endgroup$ – xavierm02 Apr 2 '13 at 21:43
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    $\begingroup$ Never mind I found out. $\$\{\}\{\}\{\}\{\}\{\}\{\}\$$ $\endgroup$ – xavierm02 Apr 2 '13 at 21:44
  • $\begingroup$ Now, we know ${}{}{}$ $\endgroup$ – Mhenni Benghorbal Apr 2 '13 at 21:58
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    $\begingroup$ All you need is a "Yes"in front of this answer, and you can win the U.S. elections! $\endgroup$ – Asaf Karagila Apr 2 '13 at 22:21
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    $\begingroup$ @Asaf: If only that didn't strike uncomfortably close to the truth.... $\endgroup$ – Cameron Buie Apr 3 '13 at 1:03

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