文档介绍：数学杂志
Journal of Mathematics
ISSN 0255-7797,CN 42-1163/O1
gs. We provide many properties and structures of these two classes
of rings by using theoretical skills in rings. The conclusions enrich the theory that related to
elements decomposition.
Keywords: UJ-ring; UQ-ring; strong UJII-ring; clean ring
2010 MR Subject Classification: 16U99; 16N20
1 Introduction
All rings considered are associative with unity. Let R be a ring. The set of all units,
the set of all idempotents and the Jacobson radical of R are denoted by U(R), idem(R)
and J(R), respectively. The symbol Mn(R) stands for the n × n matrix ring over R whose
identity element we write as In.
Rings whose elements are sums of certain special elements have been widely studied
in ring theory. Recall that a ring R is called clean if every element of R is the sum of an
idempotent and a unit. Clean rings were introduced by Nicholson [1] in relation to exchange
rings. A ring R is called strongly clean [2] if every element of R is the sum of an idempotent
and a unit that commute. According to [3, 4], a ring R is called J-clean if for each a ∈ R,
a = e + j for some e2 = e ∈ R