摘要
在文[1]中我们引进了DQrC-环,本文给出了忠实的与不忠实的DQrC-环为亚直不可约环的充分必要条件.由于DQrC-环是比DQC-环更广泛的环类,所以本文推广了W.Burgess等人在DQC-环方面相应的工作.
A ring R is called a DQr C ring if every ideal I of R is generated by I∩ Q.WhereQr={a∈R |Ra(?)aR}.For DQrC ring a faithful DQr C ring R is subdirectly irreducible,iffthere exists 0≠j∈Qr such that: (1)For all b ∈R,if such that 0≠jb∈Qr,then jRb(?)jbR; (2)R/D is a simple ring,where D=r(jR); (3)For all a ∈Qr such that aR (?)D and aR(?)jR there exists b∈R such that j=ab.
