Talk:Glossary of ring theory

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I've never heard of a "rng"; rather, the definition given for "rng" is what I've always considered a ring, and the definition given for "ring" is what I'd call a ring with identity, or a ring with 1\ne0. c.f. for example Dummit & Foote. 68.252.195.169 07:41, 27 January 2007 (UTC)

Many important terms are missing, but I am afraid that I am not able to compete it. -- Wshun

Regarding idempotent - isn't an element e of a ring idempotent if there exists some natural number n (not necessarily 2) such that e^n = e? -- Schnee 12:57, 6 Aug 2003 (UTC)

I've never seen the term defined that way. Perhaps you are confusing this with nilpotent? -- Toby Bartels 03:05, 24 Aug 2003 (UTC)

TBOMK, "idempotent" means e^2 = e, "nilpotent" means e^n = 0. Revolver

Of course, if x^2=1, then for all n, x^2n=1 and so x^(2n+1)=x. So Schnee's remark follows for odd n (only). Mousomer 26 Jan 2004

Terminology issue:

Please cite your source for the word rng, which as I mentioned earlier is the customary definition of a ring.

          S. A. G.

[edit] Zero divisor

Regarding your "If a ring has a Zero divisor which is also a unit, then the ring has no other elements and is the trivial ring", this doesn't make sense given your condition on a zero divisor that there exist a nonzero element such that... A one-element ring can't have a nonzero element and therefore can't have a zero divisor. What would be true is that no ring element can be both a zero divisor and a unit. Vaughan Pratt 22:57, 24 November 2006 (UTC)

Removed. –Pomte 17:58, 13 April 2008 (UTC)

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