Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: Description: VJM banner 

 

Home

 

Recent Issues

Volume 52

1

2

3

 

Volume 51

1

2

3

4

Volume 50

1

2

3

4

Volume 49

1

2

3

4

Volume 48

1

2

3

4

Past Issues

The Journal

Cover

Aims and Scope

Subscription Information

Editorial Board

Instructions for Author

Contact Us

 

 

Vietnam Journal of Mathematics 35:3(2007) 275-283

 Hopfian and Co-Hopfian Modules Over Commutative Rings

Kamran Divaani-Aazar and Amir Mafi

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.

 

2000 Mathematics Subject Classification: 13C05, 13E, 16D10.

Keywords: Hopfian and co-Hopfian modules, good modules, representable modules, semi Hopfian and semi co-Hopfian modules.

 

 

 

 

 

 

 

Established by Vietnam Academy of Science and Technology & Vietnam Mathematical Society

Published by Springer since January 2013