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Weakly Regular Rings

Published online by Cambridge University Press:  20 November 2018

V. S. Ramamurthi
V. S. Ramamurthi*
Affiliation:
De la Salle College, Karumathur 626514, Tamilnadu India
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This paper attempts to generalize a property of regular rings, namely,I2=I for every right (left) ideal. Rings with this property are called right (left) weakly regular. A ring which is both left and right weakly regular is called weakly regular. Kovacs in [6] proved that, for commutative rings, weak regularity and regularity are equivalent conditions and left open the question whether for arbitrary rings the two conditions are equivalent. We show in §1 that, in general weak regularity does not imply regularity. In fact, the class of weakly regular rings strictly contains the class of regular rings as well as the class of biregular rings.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 317 - 321
Copyright
Copyright © Canadian Mathematical Society 1973

References

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