✦ LIBER ✦

Free ideal rings and localization in general rings

✍ Scribed by P. M. Cohn

Book ID: 127453735
Publisher: Cambridge University Press
Year: 2006
Tongue: English
Weight: 2 MB
Series: New mathematical monographs 3
Category: Library
City: Cambridge, UK; New York
ISBN: 0511226276

No coin nor oath required. For personal study only.

✦ Synopsis

Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention.

✦ Subjects

Теория колец

📜 SIMILAR VOLUMES

Free ideal monoid rings

✍ Roman W Wong 📂 Article 📅 1978 🏛 Elsevier Science 🌐 English ⚖ 781 KB

Torsion Modules Over Free Ideal Rings

✍ Cohn, P. M. 📂 Article 📅 1967 🏛 Oxford University Press 🌐 English ⚖ 462 KB

Generating ideals in polynomial rings

✍ S. Mandal; A. Roy 📂 Article 📅 1987 🏛 Springer-Verlag 🌐 French ⚖ 283 KB

Prime Ideals in General Rings

✍ Neal H. McCoy 📂 Article 📅 1949 🏛 John Hopkins University Press 🌐 English ⚖ 902 KB

Stable ideals in Gorenstein local rings

✍ Akira Ooishi 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 438 KB

Basically Full Ideals in Local Rings

✍ William J. Heinzer; Louis J. Ratliff Jr.; David E. Rush 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 193 KB

Let A be a finitely generated module over a (Noetherian) local ring R M . We say that a nonzero submodule B of A is basically full in A if no minimal basis for B can be extended to a minimal basis of any submodule of A properly containing B. We prove that a basically full submodule of A is M-primary