Geodesic
Rings with quasi-continuous right ideals
Glasgow mathematical journal, Tome 41 (1999) no. 2, pp. 167-181

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Rings in which each right ideal is quasi-continuous (right π-rings) are shown to be a direct sum of semisimple artinian square full ring and a right square free ring. Among other results it is also shown that (i) a nonlocal right continuous indecomposable right π-ring is either simple artinian or a ring of matrices of a certain type, and (ii) an indecomposable non-local right continuous ring is both a right and a left π-ring if and only if it is a right q-ring. In particular, a non local indecomposable right q-ring is a left q-ring. 
Jain, S. K.; López-Permouth, S. R.; Syed, S. Raza. Rings with quasi-continuous right ideals. Glasgow mathematical journal, Tome 41 (1999) no. 2, pp. 167-181. doi: 10.1017/S0017089599970714
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     title = {Rings with quasi-continuous right ideals},
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     year = {1999},
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     doi = {10.1017/S0017089599970714},
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