Primary Ideals and Valuation Ideals

Primary Ideals and Valuation Ideals

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...

Almost Primary Ideals

Let R be a commutative ring with identity. In this paper we define the notion of almost primary ideal. An ideal of a ring R is said to be an almost primary ideal if for a, b ∈ R with ab ∈ I − I2 then a ∈ I or bn ∈ I for some n ∈ N. We prove that in Noetherian domains almost primary ideals are primary. Mathematics Subject Classification: 13A15

Cellular Binomial Ideals. Primary Decomposition of Binomial Ideals

It is known that algorithms exist which compute primary decompositions of polynomial ideals (Gianni et al., 1988; Eisenbud et al., 1992; Becker and Weispfenning, 1993; and more recently Shimoyama and Yokoyama, 1996). However, in case the ideal is binomial, binomiality of its primary components is not assured, that is, the above algorithms do not necessarily compute a decomposition into binomial...

z-weak ideals and prime weak ideals

In this paper, we study a generalization of z-ideals in the ring C(X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a weak ideal and naturally a weak z-ideal and a prime weak ideal are introduced and it turns out that they behave such as z-ideals in C(X).