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A note on subdirectly irreducible rings

Published online by Cambridge University Press:  17 April 2009

Madhukar G. Deshpande
Madhukar G. Deshpande
Affiliation:
Marquette University, Milwaukee, Wisconsin, USA.
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Abstract

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It is proved that every subdirectly irreducible ring can be obtained as a proper homomorphic image of another subdirectly irreducible ring. An example of a subdirectly irreducible ring R with heart H is given for which i) R has a non-subdirectly irreducible homomorphic image, ii) R/H is an integral domain, and iii) the commutator ideal C(R) of R coincides with R.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1971 , pp. 31 - 34
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Deshpande, Madhukar G., “Structure of right subdirectly irreducible rings I”, J. Algebra (to appear).Google Scholar
[2]Divinsky, Nathan, “Commutative subdirectly irreducible rings”, Proc. Amer. Math. Soc. 8 (1957), 642–648.CrossRefGoogle Scholar
[3]Moore, H.G., “Subdirectly irreducible rings - some pathology”, Bull. Austral. Math. Soc. 1 (1969), 353–355.CrossRefGoogle Scholar