A CLASS OF COMPLETE MODULES OVER A DISCRETE VALUATION DOMAIN
This thesis deals with a class of complete modules over a discrete valuation domain. A module over a discrete valuation domain is said to be complete if it is Hausdorff and every Cauchy sequence of its elements is convergent. The class of complete modules over a discrete valuation domain can be iden...
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| Institution: | Institut Teknologi Bandung |
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id-itb.:190672017-09-27T14:41:48ZA CLASS OF COMPLETE MODULES OVER A DISCRETE VALUATION DOMAIN WAYAN SWITRAYNI (NIP : 20112020); Pembimbing Dr. Hanni Garminia Y ; Prof. Dr. Pudji Astuti, NI Indonesia Theses INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/19067 This thesis deals with a class of complete modules over a discrete valuation domain. A module over a discrete valuation domain is said to be complete if it is Hausdorff and every Cauchy sequence of its elements is convergent. The class of complete modules over a discrete valuation domain can be identified through its structure; particularly the structure of a pure-injective module and the height of elements. This thesis shows that any module <br /> <br /> <br /> <br /> <br /> is complete if and only if it is a pure-injective module having no infinite height elements. The result shows that all of complete modules are contained in a class of modules, that is reduced pure-injective modules class. Furthermore, it is also shown that if a pure submodule is complete then it is a direct summand. <br /> text |
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This thesis deals with a class of complete modules over a discrete valuation domain. A module over a discrete valuation domain is said to be complete if it is Hausdorff and every Cauchy sequence of its elements is convergent. The class of complete modules over a discrete valuation domain can be identified through its structure; particularly the structure of a pure-injective module and the height of elements. This thesis shows that any module <br />
<br />
<br />
<br />
<br />
is complete if and only if it is a pure-injective module having no infinite height elements. The result shows that all of complete modules are contained in a class of modules, that is reduced pure-injective modules class. Furthermore, it is also shown that if a pure submodule is complete then it is a direct summand. <br />
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| format |
Theses |
| author |
WAYAN SWITRAYNI (NIP : 20112020); Pembimbing Dr. Hanni Garminia Y ; Prof. Dr. Pudji Astuti, NI |
| spellingShingle |
WAYAN SWITRAYNI (NIP : 20112020); Pembimbing Dr. Hanni Garminia Y ; Prof. Dr. Pudji Astuti, NI A CLASS OF COMPLETE MODULES OVER A DISCRETE VALUATION DOMAIN |
| author_facet |
WAYAN SWITRAYNI (NIP : 20112020); Pembimbing Dr. Hanni Garminia Y ; Prof. Dr. Pudji Astuti, NI |
| author_sort |
WAYAN SWITRAYNI (NIP : 20112020); Pembimbing Dr. Hanni Garminia Y ; Prof. Dr. Pudji Astuti, NI |
| title |
A CLASS OF COMPLETE MODULES OVER A DISCRETE VALUATION DOMAIN |
| title_short |
A CLASS OF COMPLETE MODULES OVER A DISCRETE VALUATION DOMAIN |
| title_full |
A CLASS OF COMPLETE MODULES OVER A DISCRETE VALUATION DOMAIN |
| title_fullStr |
A CLASS OF COMPLETE MODULES OVER A DISCRETE VALUATION DOMAIN |
| title_full_unstemmed |
A CLASS OF COMPLETE MODULES OVER A DISCRETE VALUATION DOMAIN |
| title_sort |
class of complete modules over a discrete valuation domain |
| url |
https://digilib.itb.ac.id/gdl/view/19067 |
| _version_ |
1822018831447490560 |