中科院数学与系统科学研究院
数学研究所
数论研讨班
报告人： 薛博卿 博士（中科院数学所）
题 目：Natural Monoids and Non-commutative Arithmetics
时 间：2018.12.26（星期三），16:10-17:10
地 点：数学院南楼N913室
摘 要: In this talk, we introduce several classes of monoids satisfying up to five axioms and establish basic theories on their arithmetics. The one satisfying all the axioms is named natural monoid. Two typical examples are 1) the monoid of natural numbers in the group of positive rationals and 2) a certain monoid in one of Thompson's groups. The latter one is non-abelian, which serves as an important example for non-commutative arithmetics. In particular, defining primes in a non-abelian monoid is highly non-trivial, which relies on a concept we called "castling".
