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摘要
The commutativity degree of groups and rings has been studied by certain authors since 1973, and the main result obtained is Pr(A) <= 5/8 where Pr(A) is the commutativity degree of a non-abelian group (or ring) A. Verifying this inequality for an arbitrary semigroup A is a natural question, and in this paper, by presenting an infinite class of finite non-commutative semigroups, we prove that the commutativity degree may be arbitrarily close to 1. We name this class of semigroups the almost commutative or approximately abelian semigroups.
- 出版日期2011-12
