| A ring R is called a DQrC ring if every ideal I of R is generated by I∩Qr.Where Qr={a∈R |Ra?aR}.For DQrC ring a faithful DQrC 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. |
