The Athens Algebra Seminar series presents Dr. Greg Oman on “Rings Whose Multiplicative Endomorphisms Are Power Functions, on Tuesday, Oct. 14, at 4 p.m. in Morton 226.
Oman is Assistant Professor of Mathematics at the University of Colorado at Colorado Springs.
Note that Athens Algebra Seminars is on a Tuesday. (The regular day is Thursday.)
Abstract: Let R be a commutative ring. For any positive integer m, the power function f: R→R defined by f(x):=x^m is easily seen to be an endomorphism of the multiplicative semigroup (R,*). In this talk, I will characterize the commutative rings R with identity for which every multiplicative endomorphism of (R,*) is equal to a power function. I will close with some open questions and some partial answers due to Ryzard Mazurek.
For more information, contact Dr. Sergio R. López-Permouth, Professor of Mathematics, Director of the Center of Ring Theory and its Applications (CRA) and Executive Editor of the Journal of Algebra and its Applications (JAA).
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