Talk:Glossary of ring theory

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Idempotent[edit]

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 — Preceding undated comment added 21:32, 25 November 2003 (UTC)[reply]

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

Rng[edit]

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 $1\neq 0$ . c.f. for example Dummit & Foote. 68.252.195.169 07:41, 27 January 2007 (UTC)[reply]

Many important terms are missing, but I am afraid that I am not able to compete it. -- Wshun — Preceding undated comment added 04:16, 23 June 2003 (UTC)[reply]

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

          S. A. G. — Preceding unsigned comment added by 152.163.253.98 (talk) 14:21, 10 May 2004 (UTC)[reply]

Zero divisor[edit]

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)[reply]

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

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Algebraic structures over Rngs[edit]

OK, so if I buy into this horrible idea of defining rings to have an identity (ideals aren't even subrings!), then what am I supposed to search for if I want a module defined over a rng? 129.107.61.162 (talk) 23:14, 22 April 2009 (UTC)[reply]

Every Ideal has 1 ?!?[edit]

"A subset S of the ring (R,+,*) which remains a ring when + and * are restricted to S and contains the multiplicative identity 1 of R is called a subring of R." So, every subring contains 1. ... "A left ideal I of R is a subring of R....." So every ideal is equal to R. Some native speaker should change this. —Preceding unsigned comment added by 88.70.40.178 (talk) 20:42, 1 May 2009 (UTC)[reply]