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Subdirectly irreducible rings–some pathology

Published online by Cambridge University Press:  17 April 2009

H.G. Moore
H.G. Moore
Affiliation:
Brigham Young University, Provo, Utah.
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Abstract

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Every ring is isomorphic to a subdirect sum of subdirectly irreducible rings. Unfortunately, however, as is shown, the property of being subdirectly irreducible is not preserved under homomorphisms. An example is given of a finite non-commutative subdirectly irreducible ring R with heart (= the intersection of all non-zero ideals) H, such that R/E is isomorphic with GF(2) + GF(2). (GF(2) is the two element Galois Field.) Some additional properties of the ring R are listed and contrasts are made with results for commutative subdirectly irreducible rings; for example, the zero divisors of R do not form an ideal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 353 - 355
Copyright
Copyright © Australian Mathematical Society 1969

References

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