Order ideals, annihilator ideals and pathological behavior

Annihilator-small Right Ideals

A right ideal A of a ring R is called annihilator-small if A+ T = R; T a right ideal, implies that l(T ) = 0; where l( ) indicates the left annihilator. The sum Ar of all such right ideals turns out to be a two-sided ideal that contains the Jacobson radical and the left singular ideal, and is contained in the ideal generated by the total of the ring. The ideal Ar is studied, conditions when it ...

On annihilator ideals in skew polynomial rings

This article examines annihilators in the skew polynomial ring $R[x;alpha,delta]$. A ring is strongly right $AB$ if everynon-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property ($A$) and the conditions asked by P.P. Nielsen. We assume that $R$ is an ($alpha$,$delta$)-compatible ring, and prove that, if $R$ is ni...

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...

Some pathological examples of precipitous ideals

We construct a model with an indecisive precipitous ideal and a model with a precipitous ideal with a non precipitous normal ideal below it. Such kind of examples were previously given by M. Foreman [1] and R. Laver [4] respectively. The present examples differ in two ways: firstthey use only a measurable cardinal and secondthe ideals are over a cardinal. Also a precipitous ideal without a norm...

Primary Ideals and Valuation Ideals