Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
Browse
3 results
Search Results
Master Thesis Semiperfect and Perfect Group Rings(Izmir Institute of Technology, 2014) Kalaycı, Tekgül; Pusat, DilekIn this thesis, we give a survey of necessary and sufficient conditions on a group G and a ring R for the group ring RG to be semiperfect and perfect. A ring R is called semiperfect R/RadR is semisimple and idempotents of R/RadR can be lifted to R. It is given that if RG is semiperfect, so is R. Necessary conditions on G for RG to be semiperfect are also given for some special type of groups. For the sufficient conditions, several types of rings and groups are considered. If R is commutative and G is abelian, a complete characterization is given in terms of the polynomial ring R[X]. A ring R is called left (respectively, right) perfect if R/Rad R is semisimple and Rad R is left (respectively, right) T-nilpotent. Equivalently, a ring is called left (respectively, right) perfect if R satisfies the descending chain condition on principal right (respectively, left) ideals. By using these equivalent definitions of a perfect ring and results from group theory, a complete characterization of a perfect group ring RG is given in terms of R and G.Master Thesis On δ-perfect and δ-semiperfect rings(Izmir Institute of Technology, 2014) Kızılaslan, Gonca; Pusat, DilekIn this thesis, we give a survey of generalizations of right-perfect, semiperfect and semiregular rings by considering the class of all singular R-modules in place of the class of all R-modules. For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if, whenever N +X = M with M / X singular, we have X = M. If there exists an epimorphism p : P → M such that P is projective and Ker(p) is δ-small in P, then we say that P is a projective δ-cover of M. A ring R is called δ-perfect (respectively, δ-semiperfect) if every R-module (respectively, simple R-module) has a projective δ-cover. In this thesis, various properties and characterizations of δ-perfect and δ-semiperfect rings are stated.Master Thesis Modules Whith Coprimary Decomposition(Izmir Institute of Technology, 2009) Tekin, Semra; Pusat, DilekThis thesis presents the theory of coprimary decomposition of modules over a commutative noetherian ring and its coassociated prime ideals. This theory is first introduced in 1973 by I. G. Macdonald as a dual notion of an important tool of associated primes and primary decomposition in commutative algebra. In this thesis, we studied the basic properties of coassociated prime ideals to a module M and gathered some modules in the literature which have coprimary decomposition. For example, we showed that artinian modules over commutative rings are representable. Moreover if R is a commutative noetherian ring, then we showed that injective modules over R are representable. Finally, we discussed the uniqueness properties of coprimary decomposition.