Free Modules 13 Therefore, we have the following alternative description of the strong rank condition see also Exercise For a suitable common denominator r E CR, we can 32 1. Fix an element rEm n CR. After dropping the unnecessary indices, we may therefore assume that I isfinite.
Tsit Yuen Lam
But R is not Dedekind-finite, a fortiori not stably finite. To construct a ring that has IBN but not the rank condition, we use the following matrix-theoretic characterization of the negation of the latter.
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Graduate Texts in Mathematics
Sep 07, Jamie rated it liked it Recommended to Jamie by: A graduate student friend and I have spent the better part of our graduate careers going through Lam's A First Course in Noncommutative Rings. Neither of us is a noncommutative ring theorist, so it was basically just a hobby for us that's why it has taken so long.
Actually we skipped a lot in both books there is a lot there! But we did enjoy them.
This is not bedtime reading, but it has been a good introduction for us non-specialists. View all 4 comments. Jul 16, Ryan Schwiebert rated it it was amazing.
This book features the clear exposition, excellent examples, and variety of interesting exercises that I've come to expect from Lam's books. I still enjoy this book, and it was definitely indispensable during my graduate study.
The organization and presentation really make this a pleasure to read. Adriana rated it really liked it Oct 30, Yuri Popov rated it it was amazing Apr 04, Nitin Tomar rated it it was amazing Oct 16, Muna abbas rated it it was amazing Mar 22, Wqe23 marked it as to-read Apr 15, Saeedeh marked it as to-read Nov 25, Emad Ali marked it as to-read May 12, Sukit Sangwirotjanapat added it Aug 12, Steve Dalton marked it as to-read Oct 02, Zakeiah Alkhamisi is currently reading it Dec 16, Mansour marked it as to-read Jan 05, Detektif Shilufy marked it as to-read Apr 29, LS marked it as to-read Dec 14, Hakimyousefi marked it as to-read Feb 25,