Author:
Van Truong Thi Thuy,Alghamdi Ahmad M.,Alkinani Amnah Abdu
Abstract
UDC 512.5
A ring is called a right
a
-ring if every right ideal is automorphism invariant. We describe some properties of
a
-rings over semiperfect rings. It is shown that an I-finite right
a
-ring is a direct sum of a semisimple Artinian ring and a basic ring. It is also demonstrated that if
R
is an indecomposable (as a ring) I-finite right
a
-ring not simple with nontrivial idempotents such that every minimal right ideal is a right annihilator and
S
o
c
(
R
R
)
=
S
o
c
(
R
R
)
is essential in
R
R
, then
R
is a quasi-Frobenius ring and it is also a right
q
-ring.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
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