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

For $a \neq 1$ and $p$ a prime, we define numbers of the form $pa^2$ to be Square-Prime (SP) numbers. example, $75 = 3 \cdot 25$; $108 36$; $45 5 9$. These are listed in OEIS as A228056. We study properties these numbers, their distribution/density, also develop few claims on distribution/density. rely computer programs verify some conjectures up large

In this paper, it has been proved that for a Noetherian ring R and an automorphism σ of R, an associated prime ideal of R[x, σ] or R[x, x−1, σ] is the extension of its contraction to R and this contraction is the intersection of the orbit under σ of some associated prime ideal of R. The same statement is true for minimal prime ideals also. It has also been proved that for a Noetherian Q-algebra...

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.