Right primary ideal in right duo rings

In this paper, we give a generalization of primary ideal to noncommutative ring called right primary ideal. We study the structure of right primary ideal in right andleft duo rings. A ring R is called a right (left) duo ring, if every right (left) ideal of R is a two-sided ideal. We show that in a right Noetherian left duo ring, every irreducible idealis a right primary ideal. Also, we obtain a decomposition of ideals in left duo rings. We show that every proper ideal of a right Noetherian left duo ring, is a finite intersectionof right primary ideals.

کلیدواژه ها:

Right duo ، Right primary ، Right Noetherian.