Rings whose elements are sums or minus sums of three commuting idempotents

The Sums and Products of Commuting AC-Operators

Abstract: In this paper, we exhibit new conditions for the sum of two commuting AC-operators to be again an AC-operator. In particular, this is satisfied on Hilbert space when one of them is a scalar-type spectral operator.  

Subdirect Sums of Rings

Sums of Three or More Primes

It has long been known that, under the assumption of the Riemann Hypothesis, one can give upper and lower bounds for the error ∑ p≤x log p−x in the Prime Number Theorem, such bounds being within a factor of (log x)2 of each other and this fact being equivalent to the Riemann Hypothesis. In this paper we show that, provided “Riemann Hypothesis” is replaced by “Generalized Riemann Hypothesis”, re...

Artinian Band Sums of Rings

Band sums of associative rings were introduced by Weissglass in 1973. The main theorem claims that the support of every Artinian band sum of rings is finite. This result is analogous to the well-known theorem on Artinian semigroup rings. 1991 Mathematics subject classification (Amer. Math. Soc): primary 16P20, 16W50; secondary 20M25. Let B be a band, that is, a semigroup consisting of idempoten...

Elements of Rings with Equal Spectral Idempotents

In this paper we define and study a generalized Drazin inverse x for ring elements x, and give a characterization of elements a, b for which aa = bb. We apply our results to the study of EP elements in a ring with involution. 2000 Mathematics subject classification: primary 16A32, 16A28, 15A09; secondary 46H05, 46L05.