
Vietnam
Journal of Mathematics 35:1(2007)
1119

Some
Examples of ACSRings

Qingyi Zeng

Abstract. A ring R is called a right ACSring if the annihilator of any element
in R is essential in a direct
summand of R. In this note we
will exhibit some elementary but important examples of ACSrings. Let R be a reduced ring, then R is a right ACSring if and only if
R[x] is a right ACSring. Let R
be an arigid ring. Then R is a right ACSring if and only if
the Ore extension R[x;a] is a right ACSring. A
counterexample is given to show that the upper matrix ring T_{n}(R) over a right ACSring R
need not be a right ACSring.


2000
Mathematics Subject Classification: 16E50, 16N99.

Keywords: ACSrings; annihilators;
idempotents; essential; extensions of rings.


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Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published by
Springer since January 2013

