On Duo Rings
1960 ◽
Vol 3
(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.
2019 ◽
Vol 47
(11)
◽
pp. 4533-4540
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1979 ◽
Vol 28
(4)
◽
pp. 423-426
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Keyword(s):
1983 ◽
Vol 6
(1)
◽
pp. 119-124
1973 ◽
Vol 38
(2)
◽
pp. 381-381
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