PRIME AND POISSON PRIME IDEALS IN SKEW EXTENSIONS DETERMINED BY DERIVATIONS

injective modules and prime ideals

محور اصلی این پایان نامه، r- مدولهای a – انژکتیو می باشد که آنها را به عنوان یک تعمیم از مدول های انژکتیو معرفی می کنیم. در ابتدا مدول های انژکتیو را معرفی کرده، سپس برخی نتایج مهم وشناخته شده مدول های انژکتیو را به مدول های a – انژکتیو تعمیم می دهیم. در ادامه رابطه بین مدول های a – انژکتیو و حلقه های نوتری را بررسی می کنیم. پس هدف کلی این پایان نامه این است که با بررسی انژکتیو بودن ایده آله...

Associated Prime Ideals of Skew Polynomial Rings

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...

Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings

Factoring of Prime Ideals in Galois Extensions

We return to the general AKLB setup: A is a Dedekind domain with fraction field K, L is a finite separable extension of K, and B is the integral closure of A in L. But now we add the condition that the extension L/K is normal, hence Galois. We will see shortly that the Galois assumption imposes a severe constraint on the numbers ei and fi in the ram-rel identity (4.1.6). Throughout this chapter...

Derivations in Hyperrings and Prime Hyperrings

In this paper we introduce derivations in Krasner hyperrings and derive some basic properties of derivations. We also prove that for a strongly differential hyperring $R$ and for any strongly differential hyperideal $I$ of $R,$ the factor hyperring $R/I$ is a strongly differential hyperring. Further we prove that a map $d: R rightarrow R$ is a derivation of a hyperring $R$ if and only if the in...