Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
Browse
3 results
Search Results
Master Thesis Lower-Top and Upper-Bottom Points for Any Formula in Temporal Logic(Izmir Institute of Technology, 2006) Baysal, Onur; Alizade, RafailIn temporal logic, which is a branch of modal logic, models are constructed on some kind of frames. Common properties of all these frames include totally ordered relations and these frames are bi-directional. These common properties provide the temporal logic time interpretation. By means of this interpretation temporal language has lots of application areas. The main aim of this study is to propose new technic which gets easier proof of some kind of valid formulas in the most popular temporal frame T and to produce new valid formulas with the medium of this new technic. To be able to realize this main aim, first of all the frame T . (N;6;>;R±;R for temporal language has been composed step by step in accordance with principles of modal logic. Then the new terms " lower-top and upper-bottom points for any temporal formula " has been defined in the model M . (T; V ) which is built over the frame T and some propositions of this term have been obtained. At the end of the study it has been presented that proofs of some theorems have been done easier and it has been given possibility to produce the new theorems.Moreover a general investigation about the frame T has been done and presented, furthermore it has been shown that the mirror image of the valid formulas do not have to be valid and it is also possible that the mirror image of non valid formulas can be valid.Master Thesis Generalization of Cofinitely Supplemented Modules To Lattices(Izmir Institute of Technology, 2005) Çetindil, Yasin; Alizade, RafailIn this thesis we study how to extend the notion of co¯nitely supplemented module to lattice theory. A submodule N of a module M is called co¯nite if the factor module M/N is ¯nitely generated and we say that M is a co¯nitely supplemented module if every co¯nite submodule of M has a supplement. We analogously de¯ne the notions of co¯nite element and co¯nitely supplemented lattice for lattices. Inspired by the similarities between the properties of modules and modular lattices, we obtain results for co¯nitely supplemented modular lattices, analogous to results for co¯nitely supplemented modulesMaster Thesis The Least Proper Class Containing Weak Supplement(Izmir Institute of Technology, 2009) Durğun, Yılmaz; Alizade, RafailThe main purpose of this thesis is to investigate the least proper class containing the classWS of R-modules determined by weak supplement submodules over a ring R, in particular, over hereditary rings. A submodule A of a module B has(is) weak supplement if and only if there exist a submodule V in B such that A + V . B and the intersection of submodules of A and V is small in B. The classWS does not form a proper class, in general. By extending the class WS, we obtained the least proper class containing the class WS of R-modules over hereditary rings. We investigate the homological objects of the least proper class. We determine the structure of elements of the proper class by submodules.