Idempotents in matrix rings

Authors:
Christopher Barnett and Victor Camillo

Journal:
Proc. Amer. Math. Soc. **122** (1994), 965-969

MSC:
Primary 16S50; Secondary 15A99, 16E50

MathSciNet review:
1246513

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Abstract: Let *R* be a commutative, von Neumann regular ring and the ring of matrices over *R*. What are the idempotents in ? Our motivation is to think of *R* as the sort of ring that occurs in functional analysis, for example a ring of measurable functions. We show how to uniquely write down all idempotents in in terms of arbitrary parameters. The main theorem is stated in language to appeal to an audience wider than algebraists, but in a remark, we give a more refined statement for specialists.

**[1]**Christopher Barnett and Victor Camillo,*Idempotents in matrices over commutative von Neumann regular rings*, Comm. Algebra**18**(1990), no. 11, 3905–3911. MR**1068628**, 10.1080/00927879008824115**[2]**R. S. Pierce,*Modules over commutative regular rings*, Memoirs of the American Mathematical Society, No. 70, American Mathematical Society, Providence, R.I., 1967. MR**0217056****[3]**K. R. Goodearl,*von Neumann regular rings*, Monographs and Studies in Mathematics, vol. 4, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. MR**533669**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1246513-1

Article copyright:
© Copyright 1994
American Mathematical Society