摘要
本文介绍了一类加法完全J＊-单半环,这类半环的加法半群为完全J＊-单半群.为了给出这类半环的结构,首先利用半环的H＊-类构造了一类分配夹心伪环.接着利用加法左零半环、加法右零半环和分配夹心伪环,给出了加法完全J＊-单半环的一个结构定理,推广了文献[J.Aust.Math.Soc.,1975,20（3）：257-267]中关于加法完全单半环的相关结构定理.
In this paper we introduce a class of semirings whose additive reduct is an additively completely J＊-simple semigroup. To obtain a construction of such semirings a dis-tributive sandwich skew-halfring is constructed by an H＊-class. Next, using additive left-zero semirings, additive right-zero semirings and distributive sandwich skew-halfrings, we establish a construction of additively completely J＊-simple semirings, which generalizes the main result of Grillet on semirings with a completely simple additive semigroup in [J. Aust. Math. Soc., 1975, 20（3）： 257-267] to additive non-regular semirings.
出处
《数学进展》
CSCD
北大核心
2016年第5期665-678,共14页
Advances in Mathematics（China）
基金
Supported by NSFC(No.11501237,No.11401246,No.11426112,No.61572013)
the NSF of Guangdong Province(No.2014A030310087,No.2014A030310119,No.2016A030310099)
Outstanding Young Teacher Training Program of Colleges and Universities in Guangdong Province(No.YQ2015155)
Scientific Research Innovation Team Project of Huizhou University(No.hzux1201523)
关键词
加法完全J＊-单半环
伪半环
加法左零半环
加法右零半环
REES矩阵半群
aDditively completely J＊-simple semiring
skew-halfring
additive left-zerosemiring
additive right-zero semiring
Rees matrix semigroup
