格序环的一个根的结构

On the Structure of a Radical of Lattice-Ordered Rings

英文关键词:l-Q ideal  l-Q radical  l-Q radical ring  l-Q semisimple ring.

中文摘要:

      从不同角度刻画了格序环Ｒ的Ｐ－根和ｌ－Ｂ根，并对ｌ－Ｑ根环进行了讨论．揭示了Ｒ及Ｒ上的全矩阵环Ｒｎ的ｌ－Ｑ根，ｌ－Ｑ理想，素ｌ－理想，半素ｌ－理想之间的关系．

英文摘要:

      We describe the P-radical and the l-B radical of an l- ring from a different angle and obtain the structure theorem of l-Qsemisimple rings. Furthermore, l-Q radical rings are discussed. Lastly, we consider the l-Q radical Q(R_n) of a full l-matrix l- ring R_n over an l-ring R. We show that Q(R_n)=(Q(R)) n.