If R is an infinite cyclic ring (, the behavior of R is a nonnegative integer k such that there exists a generatorPlanetmathPlanetmathPlanetmath ( r of the additive groupMathworldPlanetmath of R with r2=kr.

If R is a finite cyclic ring of order n, the behavior of R is a positive divisorMathworldPlanetmathPlanetmath k of n such that there exists a generator r of the additive group of R with r2=kr.

For any cyclic ring, behavior exists uniquely. Moreover, the behavior of a cyclic ring determines many of its .

To the best of my knowledge, this definition first appeared in my master’s thesis:

Buck, Warren. Rings. Charleston, IL: Eastern Illinois University, 2004.

Title behavior
Canonical name Behavior
Date of creation 2013-03-22 16:02:29
Last modified on 2013-03-22 16:02:29
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 15
Author Wkbj79 (1863)
Entry type Definition
Classification msc 13A99
Classification msc 16U99