Open Question: Abstract Algebra: Rings: Idempotents and Nilpotents...?
22:54 Publicado por Flechado16
Let R be a ring, where r is an element of R.
Let e = e^2 by an idempotent in R.
Let e = e^2 by an idempotent in R.
1. Show that er(1-e) and (1-e)re are nilpotents for every r in R.
2. Show that e + er(1-e) and e + (1-e)re are idempotents for every r in R.
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