拟正则双序集用矩形双序集的余扩张

Coextensions of Quasi-regular Biordered Sets by Rectangular Biordered Sets

称双序集E为双序集F用矩形双序集的余扩张，若存在满双序集态射θ：E→F，使对每个α∈F，αθ－1是E的矩形双序子集．本文讨论了拟正则双序集的这种余扩张的性质，给出了它们的结构．作为应用，证明了拟正则的硬双序集实为正则双序集．

Abiordered set E is called a coextension of a biordered set F by rectangularbiordered sets, if there exists a surjective biordered set morphism θ: E → F suchthat, for each α∈F, αθ-1 is a rectangular biordered subset of E. In this paper,suchcoextensions for quasi-regular biordered sets are discussed, a construction of them isgiven. As an application, it is proved that quasi-regular and solid biordered sets are infact regular.