Geodesic
On Duo Rings
Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 167-172

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Following E. H. Feller [l], a ring R is called a duo ring if every one-sided ideal of R is a two-sided ideal.In the first part of this paper, we give some properties of duo rings and we show that the set of the nilpotent elements of a duo ring R is an ideal, the intersection of the completely prime ideals of R.It is easy to see that every duo ring is a subdirect sum of subdirectly irreducible duo rings. We give in the second part of this paper a characterization of the subdirectly irreducible duo rings. This characterization is quite similar to the characterization of the subdirectly irreducible commutative rings, due to N. H. McCoy [2], whose methods we use. 
Thierrin, G. On Duo Rings. Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 167-172. doi: 10.4153/CMB-1960-021-7
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[1] 1. Feller, E. H., Properties of primary noneommutative rings, Trans. Amer. Math. Soc. 89 (1958), 79-91. Google Scholar

[2] 2. McCoy, N. H., Subdirectly irreducible commutative rings, Duke Math. J. 12 (1945), 381-387. Google Scholar

[3] 3. McCoy, N. H., Prime ideals in general rings, Amer. J. Math. 71 (1949), 823-833.10.2307/2372366 Google Scholar

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