behavior

If $R$ is an infinite cyclic ring (http://planetmath.org/CyclicRing3), the behavior of $R$ is a nonnegative integer $k$ such that there exists a generator (http://planetmath.org/Generator) $r$ of the additive group of $R$ with $r^{2}=kr$ .

If $R$ is a finite cyclic ring of order $n$ , the behavior of $R$ is a positive divisor $k$ of $n$ such that there exists a generator $r$ of the additive group of $R$ with $r^{2}=kr$ .

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. http://planetmath.org/?op=getobj&from=papers&id=336Cyclic Rings. Charleston, IL: Eastern Illinois University, 2004.

单词	Behavior
释义	behavior If $R$ is an infinite cyclic ring (http://planetmath.org/CyclicRing3), the behavior of $R$ is a nonnegative integer $k$ such that there exists a generator (http://planetmath.org/Generator) $r$ of the additive group of $R$ with $r^{2}=kr$ . If $R$ is a finite cyclic ring of order $n$ , the behavior of $R$ is a positive divisor $k$ of $n$ such that there exists a generator $r$ of the additive group of $R$ with $r^{2}=kr$ . 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. http://planetmath.org/?op=getobj&from=papers&id=336Cyclic Rings. Charleston, IL: Eastern Illinois University, 2004.
随便看	CounterexampleToTonellisTheorem counter-example to Tonelli’s theorem CountingComplexityClass counting complexity class CountingCompositionsOfAnInteger counting compositions of an integer CountingMeasure counting measure CountingProblem counting problem CountingProcess counting process CountingTheorem counting theorem CourseofvaluesRecursion course-of-values recursion Covariance covariance CovarianceMatrix covariance matrix Covector covector Cover cover CoveringSpace