The set of all endomorphisms over -module is a non-empty denoted by . From we can construct the ring addition and composition function. prime ideal an which satisfies properties like numbers. In this paper, take integer number module such that ring. Furthermore, show existences on We also applied property to

In this paper we exhibit some examples of non-Gorenstein Hecke algebras, and hence some modular forms for which mod 2 multiplicity one does not hold. Define S2(Γ0(N)) to be the space of classical cuspidal modular forms of weight 2, level N , and trivial character. The Hecke algebra TN is defined to be the subring of End(S2(Γ0(N)) generated by the Hecke operators {Tp : p 6 |N} and {Uq : q|N}. Le...

Aghapournahr and Melkersson introduced the notion of condition on a Serre subcategory category modules over commutative Noetherian ring. This paper investigates structure set prime ideals satisfying subcategory. We try to calculate members this for consisting extension in two given subcategories. Moreover, we classify sets rings with small dimension.