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Relating Properties of a Ring and Its Ring of Row and Column Finite Matrices

✍ Scribed by Victor Camillo; F.J Costa-Cano; J.J Simón

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
117 KB
Volume
244
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Mackey and Ornstein proved that if R is a semi-simple ring then the ring of row Ž Ž . . and column finite matrices over R RCFM R is a Baer ring for any infinite set ⌫ Ž . ⌫. A ring with identity is a Baer ring if every left equivalent every right annihilator is generated by an idempotent. This result is discussed in Kaplansky's book, ''Rings of Operators.'' This result is of course decades old. Here we prove that the converse is true. The proof is long and we develop techniques which allow Ž . us to obtain results of a more modern flavor about RCFM R , where R is a ⌫ perfect or semi-primary ring. Finally, we obtain good enough results on annihila-Ž . tors in RCFM ‫ޚ‬ to show that this ring is coherent.

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