Errata and Addenda

An error has been kindly pointed out to the author by Prof. K. Veradarajan and hence one needs to split original Theorem 5.1 into two theorems.

Theorem 5.1

Let R be a ring and x an element in R. If x is an element of R and x = a + 1, where a is periodic, then x is clean.

Theorem 5.2

Let R be an algebra over a field F of characteristic zero. If x is an element of R and if x = a − 1, where a is periodic, then x is clean.

Corollary 5.1

Let R be an algebra over a field F of characteristic zero. If each element in R is a sum of periodic element and 1 and −1, then R is clean.

Notes

Communicated by K. Misra.