中文摘要：

研究了圈的正则自同态幺半群的格林关系,刻画了圈的正则D-类图,并讨论了一些相关的计数问题.同时也确定了圈的自同态幺半群的完全正则性.

英文摘要：

The regular endomorphism monoid of circuits is firstly considered, then the Green＇s relations on regular circuits is characterized, and then the complete regularity of the endomorphism monoid of circuits is determined. In addition, the cardinalities of the automorphism and endomorphism of regular circuits is computed.