𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Ideal Theory of Right Cones and Associated Rings

✍ Scribed by Hans-Heinrich Brungs; Günter Törner

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
197 KB
Volume
210
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Right cones are semigroups with a left cancellation law such that for any two elements a, b there exists an element c with b s ac or a s bc. Valuation rings, cones of ordered or left ordered groups, semigroups of ordinal numbers, and Hjelmslev rings are examples. The ideal theory of these semigroups is described in terms of prime and completely prime ideals, and a classification of prime segments is given that can be used to solve a problem raised by Skornyakov. The Archimedean case can be dealt with in a satisfactory way with the help of Holder's theorem. Right cones of rank 1 are classified. We then consider the problem of constructing for a given right cone H a right chain ring R with the same right ideal and ideal structure as H.

📜 SIMILAR VOLUMES

Rings of Operators on Modules over Commu
Rings of Operators on Modules over Commutative Rings and Their Right Ideals
✍ R.C Cannings; M.P Holland 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 300 KB

We introduce and impose conditions under which the finitely generated essential right ideals of E may be classified in terms of k-submodules of M. This yields a classification of the domains Morita equivalent to E when E is a Noetherian domain. For example, a special case of our results is:

Gorenstein Associated Graded Rings of An
Gorenstein Associated Graded Rings of Analytic Deviation Two Ideals
✍ Shiro Goto; Shin-ichiro Iai 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 146 KB

This paper studies the question of when the associated graded ring I = n≥0 I n /I n+1 of a certain ideal I in a local ring is Gorenstein. The main result implies, for example, that if A is a regular local ring, is a prime ideal in A with dim A/ = 2, and A/ is a complete intersection in codimension o