Wikipedia:Reference desk/Archives/Mathematics/2018 October 18

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October 18

Rings with characteristic a prime power

What do rings with characteristic a prime to a power greater than 1 behave like, vs. those with characteristic a squarefree integer? I mean, no nilpotent elements when it’s a squarefree characteristic, true? Are there books or chapters in books about this?Rich (talk) 00:08, 18 October 2018 (UTC)

Pretty sure you can have nilpotent elements whatever the characteristic, e.g. x in Q[x]/<x²>. Almost any text on commutative algebra will have information on nilpototent elements and the nilradical, probably not much specifically on rings with non-squarefree (square having?) characteristic; it depends on what ring theorists consider interesting and/or useful. --RDBury (talk) 23:21, 18 October 2018 (UTC)

maybe i have forgotten so much that i don’t even realize what i’ve forgotten, but in your Q[x] mod x^2, although x^2 is indeed 0, i meant the addition operation. well, i better review!Rich (talk) 22:29, 21 October 2018 (UTC)

Calculator language

Someone has pointed out that if you write pi to two places of decimals (3.14, closing up the 4) and hold the paper to a mirror you see the word "pie". Are there any similar coincidences? 92.8.223.143 (talk) 11:18, 18 October 2018 (UTC)

We have the article Mathematical coincidence which is maybe of interest. Staecker (talk) 12:39, 18 October 2018 (UTC)