✦ LIBER ✦

Lazy bases: a minimalist constructive theory of Noetherian rings

✍ Scribed by Hervé Perdry

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 158 KB
Volume: 54
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200710042

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We give a constructive treatment of the theory of Noetherian rings. We avoid the usual restriction to coherent rings; we can even deal with non‐discrete rings. We introduce the concept of rings with certifiable equality which covers discrete rings and much more. A ring R with certifiable equality can be fitted with a partial ideal membership test for ideals of R. Lazy bases of ideals of R [X ] are introduced in order to derive a partial ideal membership test for ideals of R [X ]. It is then proved that if R is Noetherian, then so is R [X ]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

ChemInform Abstract: A New Carvone Based

ChemInform Abstract: A New Carvone Based Construction of the Ring-A of Taxoids.

✍ Goverdhan Mehta; Shital K. Chattopadhyay; Jayant D. Umarye 📂 Article 📅 2010 🏛 John Wiley and Sons ⚖ 23 KB 👁 1 views

ChemInform Abstract: Total Synthesis of

ChemInform Abstract: Total Synthesis of (S)-(-)-Curvularin (III): A Ring Closing Metathesis Based Construction of the Macrocyclic Framework.

✍ Debendra K. Mohapatra; Hasibur Rahaman; Rita Pal; Mukund K. Gurjar 📂 Article 📅 2008 🏛 John Wiley and Sons ⚖ 26 KB 👁 1 views

Oxidative Cyclization Based on Reversing

Oxidative Cyclization Based on Reversing the Polarity of Enol Ethers and Ketene Dithioacetals. Construction of a Tetrahydrofuran Ring and Application to the Synthesis of (+)-Nemorensic Acid.

✍ Bin Liu; Shengquan Duan; Angela C. Sutterer; Kevin D. Moeller 📂 Article 📅 2003 🏛 John Wiley and Sons ⚖ 354 KB 👁 2 views

Stereoselective Construction of 3a-Methy

Stereoselective Construction of 3a-Methylhydrindans Starting from 2,7-Enynol Derivatives Based on Ti(II)-Mediated Cyclization and Ru-Catalyzed Ring-Closing Metathesis.

✍ Mutsumi Ohkubo; Wataru Uchikawa; Hitomi Matsushita; Aiko Nakano; Takayuki Shirat 📂 Article 📅 2006 🏛 John Wiley and Sons ⚖ 38 KB

Synthesis of 5-Methylindole-4,7-quinone

Synthesis of 5-Methylindole-4,7-quinone Through a New Construction of the Functionalized Indole Ring Based on the Allene-Mediated Electrocyclic Reaction Involving the Pyrrole[b]-Bond.

✍ Maho Hirayama; Tominari Choshi; Teppei Kumemura; Shigeo Tohyama; Junko Nobuhiro; 📂 Article 📅 2004 🏛 John Wiley and Sons ⚖ 19 KB 👁 2 views

ChemInform Abstract: A Novel Method of I

ChemInform Abstract: A Novel Method of Indole Ring System Construction: One-Pot Synthesis of 4- and 6-Nitroindole Derivatives via Base-Promoted Reaction Between 3-Nitroaniline and Ketones.

✍ Nikolai Moskalev; Mieczyslaw Makosza 📂 Article 📅 2010 🏛 John Wiley and Sons ⚖ 30 KB 👁 2 views