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Modules Whith Coprimary Decomposition
(Izmir Institute of Technology, 2009) Tekin, Semra; Pusat, Dilek
This 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.

Master Degree / Yüksek Lisans Tezleri