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Title: | Pseudo Principally Quasi-Injective Modules And Pseudo Quasi-Principally Injective Modules |

Authors: | Nonthit Goonwises |

Keywords: | Modules (Algebra) |

Issue Date: | 2012 |

Publisher: | Rajamangala University of Technology Thanyaburi. Faculty of Science and Technology |

Abstract: | The purposes of this thesis are to (1) study the properties and characterizations of pseudo principally quasi-injective modules and pseudo quasi-principally injective modules, (2) study the properties and characterizations of endomorphism rings of the two types of modules, (3) extend the concepts of principally quasi-injective modules and quasi-principally injective modules and (4) find some relations between among the four types of modules mentioned. Let R be a ring. A right R-module M is called principally injective if every R-homomorphism from a principal right ideal of R to M can be extended to an R-homomorphism from R to M. A right R-module N is called principally M-injective if every R-homomorphism from a principal submodule of M to N can be extended to an R-homomorphism from M to N. A right R-module M is called principally quasi-injective if it is principally M-injective. A right R-module N is called M-principally injective if every R-homomorphism from an M-cyclic submodule of M to N can be extended to an R-homomorphism from M to N. A right R-module M is called quasi-principally injective if it is M-principally injective. The notion of principally quasi-injective modules and quasi-principally injective modules are extended to be pseudo principally quasi-injective modules and pseudo quasi-principally injective modules, respectively. A right R-module N is called pseudo principally M-injective if every R-monomorphism from a principal submodule of M to N can be extended to an R-homomorphism from M to N. A right R-module M is called pseudo principally qausi-injective if it is pseudo principally M-injective. A right R-module N is called pseudo M-principally injective if every R-monomorphism from an M-cyclic submodule of M to N can be extended to an R-homomorphism from M to N. A right R-module M is called pseudo qausi-principally injective if it is pseudo M-principally injective… |

URI: | http://www.repository.rmutt.ac.th/dspace/handle/123456789/1287 |

Appears in Collections: | วิทยานิพนธ์ (Thesis - SCI) |

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131791.pdf | Pseudo Principally Quasi-Injective Modules And Pseudo Quasi-Principally Injective Modules | 1.73 MB | Adobe PDF | View/Open |

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