■—正则半群与一致和反一致特征部分带

ON ■—REGULAR SEMIGROUPS AND UNIFORM AND ANTIUNIFORM CHARACTERISTIC PARTIAL BANDS

研究■—正则半群与一致和反一致特征部分带间的关系。由一致特征鄙分带构造双单■—正则半群和由反一致特征部分带构造其为完全正则半群的■—正则半群,所得结果推广了Howie和Schein与Munn的关于半格与逆半群以及Hall的关于带和纯整半群的相应结果,并且部分地回答了Bairad的一公开问题。

In this paper, the relation between ■—regular semigroups and uniform and antiuniform characteristic partial bands is studied. Bisimple■—regular semigroups can be construted from unifom characteristic partial bands, and only ■—regular semigroups which are completely regular semigroups can be constructed forom antiuniform characteristic partial bands. The results obtained in this paper are generalizations of the corresponding results for semilattices and inverse semigroups, which are due to Howie and Schein and Munn, and for bands and orthodox semigroups, which due to Hall. One of the results gives a partial answer to a question raised by Baird.