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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Ring Construction - Any Simple Examples Welcome
Replies: 2   Last Post: Nov 22, 2012 7:26 PM

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eric.fennessey@gmail.com

Posts: 4
Registered: 11/22/12
Ring Construction - Any Simple Examples Welcome
Posted: Nov 22, 2012 5:49 AM
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I have been looking at periodic linear recurrences and have some conditions involving roots of unity. Now I can get the same results out in the context of a Ring if I assume that I have two elements r and s with the following properties:-

1) r and s commute
2) r^n = s^m = 1_R (i.e. they are 'roots' of the multiplicative identity)
3) r - s is not a zero divisor

Unfortunately my ring theory is not strong enough to identify any examples other than the complex numbers which were what I was trying to abstract in the first place. Can anyone help, or point out why I shouldn't expect more exotic examples to exist?

Regards,
Eric

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