… study strongly duo modules over commutative rings and investigate when a duo module is a
strongly duo module or a strongly duo … ring of a strongly duo module, and show that reduced …

… In addition, if R is a Noetherian quasi-injective ring, then R is strongly duo if … strongly
duo rings are precisely semisimple rings. Moreover, if R is a perfect ring, then uniserial R-modules …

… Utumi-module (in fact it is dual-square-free). In particular, every right quasi-duo ring (a ring
where … Suppose R = S × T, where S is a semisimple ring and T is a strongly regular ring. Then, …

… : factor rings of R[r] are strongly hounded. Finally we consider the foriiial power series ring
R[[.r]] over a strongly regular ring R and prove that if R is self-injective tllen R[[x]] is right duo. …

… both right duo rings and unique-simple-module rings as members of a larger class of rings
… It is known [9, Theorem 7] that R is a strongly regular ring if and only if R is a regular duo ring…

… says that for a weakly right duo ring R, if every prime ideal … duo ring R, if the prime radical
P(R) = 0 and every prime ideal of R is maximal, then R is ^--regular. A ring R is called strongly …

… Obviously left duo rings satisfy (**). Recall that R is called SLB (strongly left bounded) ring if
… We will show that the polynomial ring R = lII[x] is not left duo but SLB. Then Proposition 3.1. …

… modules over a large class of duo rings. We also give an upper bound for the length of a duo
ring R in terms of the length of a faithful R-module. … ℵ 0 selfinjective strongly regular ring (for …

… ) if and only if R is a direct product of a semisimple Artinian ring and a strongly regular ring.
… Since semisimple Artinian rings and strongly regular rings are all essentially right duo, the …

… , which is compared with the fact that Abelian regular rings are duo. For a right π-duo ring R,
it is shown that every prime ideal of R is maximal if and only if R is a (strongly) π-regular ring …