Speaker: Professor Pete Johnson

 

Title: Generalized Frobenius Problems: How One Variety of These Came to Exist

Abstract:  A typical Frobenius problem is of this form:  Given relatively prime positive integers a(1), ... ,a(n), find the largest integer which is not expressible as a linear combination of the a(i) with non-negative integer coefficients.  Such a largest integer exists by a 19th century theorem somewhat inaccurately attributed to Frobenius.  The talk will describe the development of a generalization of such problems, and of that theorem, to arbitrary commutative rings with unit, and to modules over such rings.