U.S.-Australian Cooperative Research: Categories, Languages and Completely Regular Semigroup Varieties

该奖项支持马奎特大学的彼得·R·琼斯博士访问霍巴特的塔斯马尼亚大学，与彼得·G·特罗特博士在涉及半群的数论领域进行合作。研究人员计划合并半群理论研究的两个领域，这两个领域在过去十年中取得了最大的进展，但其发展几乎完全独立。第一种是“有限”半群理论，它源于形式语言、自动机和有限半群之间的显式联系。另一种是完全正则半群理论--那些是其子群的并的理论，对它的研究最近又重新兴起。每个领域最近的重要发展将被应用到另一个领域，特别是Polak关于簇的分解理论将被应用于有限半群理论，而态射的“派生范畴”将被应用于完全正则半群理论。关键的融合将涉及对完全规则么半群的“局部”变种的系统研究。

This award supports a visit by Dr. Peter R. Jones of Marquette University to the University of Tasmania, in Hobart, to work with Dr. Peter G. Trotter on an area of number theory involving semigroups. The investigators plan to merge two areas of semigroup theory research which have seen the greatest advances over the past decade, but whose development has been almost completely independent. The first is "finite" semigroup theory, which arises from the explicit connections among formal languages, automata and finite semigroups. The other is the theory of completely regular semigroups--those which are unions of their subgroups, and research on which has seen a resurgence of late. Important recent developments in each field will be applied to the other, notably Polak's decomposition theory for varieties will be applied to finite semigroup theory, and the "derived category" of a morphism will be applied to completely regular semigroup theory. The key fusion will involve a systematic study of the "local" varieties of completely regular monoids.