HEREDITARY AND COHEREDITARY STRUCTURES

This dissertation deals with hereditary and cohereditary properties of algebraic systems such as algebras, modules, coalgebras and comodules. The main contribution of the result is an interrelation of hereditary and cohereditary structures with other properties such as Dedekind and strongly prime an...

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主要作者: GARMINIA Y. (NIM 30104002), HANNI
格式: Dissertations
語言:Indonesia
在線閱讀:https://digilib.itb.ac.id/gdl/view/10545
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機構: Institut Teknologi Bandung
語言: Indonesia
id id-itb.:10545
spelling id-itb.:105452017-09-27T15:45:36ZHEREDITARY AND COHEREDITARY STRUCTURES GARMINIA Y. (NIM 30104002), HANNI Indonesia Dissertations INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/10545 This dissertation deals with hereditary and cohereditary properties of algebraic systems such as algebras, modules, coalgebras and comodules. The main contribution of the result is an interrelation of hereditary and cohereditary structures with other properties such as Dedekind and strongly prime and generalization some existing results in literature to the larger classes concerning hereditary and cohereditary properties. The categorical used is applied to develop the results on module and comodule areas.<p> In this dissertation, we investigate on interconection between Dedekind modules and hereditary Noetherian prime (HNP) modules. Particularly, it is shown that any projective Dedekind module is an HNP module. The result is a main contribution of the dissertation in the module theory. It is also shown that the quotient module of a Dedekind module is a Dedekind module. The connection between hereditary modules in o[M] and the projective in o[M] is studied. In this dissertation we investigate the characterizations of a hereditary module connected to a projective module in o[M].<p>The main result of the dissertation in the comodule theory is about a connection between hereditary coalgebras and hereditary algebras over a commutative self injective ring. Particularly, the dual structure of a cohereditary coalgebra is a hereditary algebra and vice versa. These properties are developed through an auxiliary result; that is any coalgebra being cohereditary if and only if its global dimension being less than or equal to 1. For a coalgebra over a commutative self injective cogenerator ring, it is shown that if its dual is a Dedekind algebra, then the coalgebra is cohereditary strongly coprime. In this dissertation we derive some hereditary and cohereditary properties over a commutative ring; those are the characterization and the direct sum of cohereditary comodule. Further, we apply the results to coalgebras over a commutative ring. text
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country Indonesia
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description This dissertation deals with hereditary and cohereditary properties of algebraic systems such as algebras, modules, coalgebras and comodules. The main contribution of the result is an interrelation of hereditary and cohereditary structures with other properties such as Dedekind and strongly prime and generalization some existing results in literature to the larger classes concerning hereditary and cohereditary properties. The categorical used is applied to develop the results on module and comodule areas.<p> In this dissertation, we investigate on interconection between Dedekind modules and hereditary Noetherian prime (HNP) modules. Particularly, it is shown that any projective Dedekind module is an HNP module. The result is a main contribution of the dissertation in the module theory. It is also shown that the quotient module of a Dedekind module is a Dedekind module. The connection between hereditary modules in o[M] and the projective in o[M] is studied. In this dissertation we investigate the characterizations of a hereditary module connected to a projective module in o[M].<p>The main result of the dissertation in the comodule theory is about a connection between hereditary coalgebras and hereditary algebras over a commutative self injective ring. Particularly, the dual structure of a cohereditary coalgebra is a hereditary algebra and vice versa. These properties are developed through an auxiliary result; that is any coalgebra being cohereditary if and only if its global dimension being less than or equal to 1. For a coalgebra over a commutative self injective cogenerator ring, it is shown that if its dual is a Dedekind algebra, then the coalgebra is cohereditary strongly coprime. In this dissertation we derive some hereditary and cohereditary properties over a commutative ring; those are the characterization and the direct sum of cohereditary comodule. Further, we apply the results to coalgebras over a commutative ring.
format Dissertations
author GARMINIA Y. (NIM 30104002), HANNI
spellingShingle GARMINIA Y. (NIM 30104002), HANNI
HEREDITARY AND COHEREDITARY STRUCTURES
author_facet GARMINIA Y. (NIM 30104002), HANNI
author_sort GARMINIA Y. (NIM 30104002), HANNI
title HEREDITARY AND COHEREDITARY STRUCTURES
title_short HEREDITARY AND COHEREDITARY STRUCTURES
title_full HEREDITARY AND COHEREDITARY STRUCTURES
title_fullStr HEREDITARY AND COHEREDITARY STRUCTURES
title_full_unstemmed HEREDITARY AND COHEREDITARY STRUCTURES
title_sort hereditary and cohereditary structures
url https://digilib.itb.ac.id/gdl/view/10545
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