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Vietnam Journal of Mathematics 35:3(2007)
275-283
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Hopfian and Co-Hopfian Modules Over
Commutative Rings
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Kamran
Divaani-Aazar and Amir Mafi
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Abstract. The structures of Hopfian and
co-Hopfian modules over commutative rings are studied. The notation of semi
Hopfian (resp. semi co-Hopfian) modules as a generalization of that of
Hopfian (resp. co-Hopfian) modules was introduced in [2]. A
characterization of semi Hopfian modules by using certain sets of prime
ideals is given. Also, it is shown the analogue of Hilbert's Basis Theorem
is valid for semi Hopficity, to the effect that an R-module M is semi
Hopfian if and only if M[X] is a semi Hopfian R[X] -module. Moreover, we shall prove the dual of these results
for semi co-Hopfian modules.
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2000 Mathematics Subject Classification: 13C05, 13E,
16D10.
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Keywords: Hopfian and co-Hopfian modules, good
modules, representable modules, semi Hopfian and semi co-Hopfian modules.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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