2015/10/20 by Edgar E. Enochs, Edgar Enochs, Overtoun M. G. Jenda +5
Computer Science · Mathematics · #Advanced Algebra and Logic #Logic, programming, and type systems #math.RA #msc:13F25 #msc:16W60 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1510.05984
arxiv created 2015/10/20 · arxiv updated 2015/10/21
Formal power series come up in several areas such as formal language theory , algebraic and enumerative combinatorics, semigroup theory, number theory etc. This paper focuses on the set x R[[x]] consisting of formal power series with zero constant term. This subset forms a monoid with the composition operation on series. We classify the sets T of strictly positive integers for which the set of formal power series, R[[xT]]=all formal power series consisting of terms whose power is from T, forms a monoid with composition as the operation. We prove that in order for R[[xT]] to be a monoid, T itself has to be a submonoid of N. Unfortunately, this condition is not enough to guarantee the desired result. But if a monoid is strongly closed, then we get the desired result. We also consider an analogous problem for power series in several variables.