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Compressible matrix rings

Published online by Cambridge University Press:  17 April 2009

Efraim P. Armendariz  and
Jae Keol Park
Efraim P. Armendariz
Affiliation:
Department of Mathematics, University of Texas, Austin, Texas 78712, U.S.A.
Jae Keol Park
Affiliation:
Department of Mathematics, Busan National University, Busan 607, Korea.
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Abstract

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Let Z(K) denote the center of a ring K. A ring R is compressible if Z(eRe) = eZ(R) for each idempotent e of R. In response to a question of S. Berberian, G. Bergman has constructed a (non-commutative) integral domain, satisfying a polynomial identity, for which the 2×2 matrix ring over the domain is not compressible. In contrast to Bergman's example, we show that the ring of nxn matrices over any commutative ring is always compressible.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 2 , October 1984 , pp. 295 - 298
Copyright
Copyright © Australian Mathematical Society 1984

References

REFERENCES

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[2]Bergman, G.M., “Some examples of non-compressible rings”, Comm. in Algebra 12 (1984), 1–8.CrossRefGoogle Scholar
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