JP Journal of Algebra, Number Theory and Applications
Volume 11, Issue 2, Pages 159 - 167
(August 2008)
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QUASI-PROJECTIVE MODULES WITH STRONGLY REGULAR ENDOMORPHISM RINGS
K. Varadarajan (Canada)
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Abstract: Let M be a finitely generated quasi-projective module. For any such Mwe prove the following results:
(i) Every quotient module N of M is is strongly p-regular.
(ii) Every quotient module N of M is simultaneously Hopfian and is strongly p-regular for every quotient N of M.
We give an example of a non-finitely generated quasi-projective abelian group A with every factor group of A simultaneously Hopfian and co-Hopfian but not strongly p-regular. We also introduce the concept of a primitive module and show that if L is any module satisfying with all primitive quotients of L Hopfian, then L itself is Hopfian. In particular any V-module L with Hopfian primitive quotients is itself Hopfian. |
Keywords and phrases: Hopfian modules, co-Hopfian modules, strongly p-regular rings,V-modules. |
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