BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, vol.26, no.4, pp.619-631, 2019 (SCI-Expanded)
In this paper we introduce a new class of rings whose elements are a sum of a central and a unit element, namely a ring R is called CU if each element a is an element of R has a decomposition a = c + u where c is central and u is unit. One of the main results in this paper is that if F is a field which is not isomorphic to Z(2), then M-2(F) is a CU ring. This implies, in particular, that any square matrix over a field which is not isomorphic to Z(2) is the sum of a central matrix and a unit matrix.