Sums of units in self-injective rings

We prove that if no field of order less than n + 2 is a homomorphic image of a right self-injective ring R, then for any element a ∈ R and central units u1, u2, …, un ∈ U(R) there exists a unit u ∈ U(R) such that a + uiu ∈ U(R) for each i ≥ 1.

NOTE ON SUMS OF UNITS IN REAL CUBIC FIELDS

ABSTRACT Let K/Q be a cyclic cubic field with an prime conductor l. In the paper there is given method for verification that K is ω-good and it is applied for conductors up to l = 349.

SUMS OF UNITS IN RINGS

In this paper, we study rings that are additively generated by units. We prove that if the identity in a ring with stable range one is a sum of two units, then every (von Neumann) regular element is a sum of two units. It follows that every element in a unit-regular ring is a sum of two units if the identity is a sum of two units. Also, if the identity of a strongly π-regular ring is a sum of two units, then every element is a sum of three units.

Addendum to “Ring elements as sums of units”

We give a comment to Theorem 1.1 published in our paper “Ring elements as sums of units” [Cent. Eur. J. Math., 2009, 7(3), 395–399].