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Change of ring and torsion-theoretic injectivity

Published online by Cambridge University Press:  17 April 2009

Iuliu Crivei ,
Septimiu Crivei  and
Ioan Purdea
Iuliu Crivei
Affiliation:
Department of Mathematics, Technical University, Str. C. Daicoviciu 15, 400020 Cluj-Napoca, Romania, e-mail: crivei@math.utcluj.ro
Septimiu Crivei
Affiliation:
Faculty of Mathematics and Computer Science, “Babeş-Bolyai” University, Str. M. Kogălniceanu 1, 400084 Cluj-Napoca, Romania, e-mail: purdea@math.ubbcluj.ro
Ioan Purdea
Affiliation:
Faculty of Mathematics and Computer Science, “Babeş,-Bolyai” University, Str. M. Kogălniceanu 1, 400084 Cluj-Napoca, Romania, e-mail: crivei@math.ubbcluj.ro
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Let τ be a hereditary torsion theory in R-Mod. Then any ring homomorphism γ: R → S induces in S-Mod a torsion theory σ given by the condition that a left S-module is σ-torsion if and only if it is τ-torsion as a left R-module. We show that if γ: R → S is a ring epimorphism and A is a τ-injective left R-module, then AnnA Ker(γ) is σ-injective as a left S-module. As a consequence, we relate τ-injectivity and σ-injectivity, and we give some applications.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 1 , February 2007 , pp. 127 - 133
Copyright
Copyright © Australian Mathematical Society 2007

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