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Rings with quasi-continuous right ideals

Published online by Cambridge University Press:  19 July 2001

S. K. Jain ,
S. R. López-Permouth  and
S. Raza Syed
S. K. Jain
Affiliation:
Ohio University, Athens, Ohio 45701, USA
S. R. López-Permouth
Affiliation:
Ohio University, Athens, Ohio 45701, USA
S. Raza Syed
Affiliation:
Ohio University, Athens, Ohio 45701, USA
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Abstract

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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 2 , May 1999 , pp. 167 - 181
Copyright
1999 Glasgow Mathematical Journal Trust