Geodesic
On the automorphism-invariance of finitely generated ideals and formal matrix rings
Filomat, Tome 37 (2023) no. 29, p. 9961

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DOI

In this paper, we study rings having the property that every finitely generated right ideal is automorphism-invariant. Such rings are called right f a-rings. It is shown that a right f a-ring with finite Goldie dimension is a direct sum of a semisimple artinian ring and a basic semiperfect ring. Assume that R is a right f a-ring with finite Goldie dimension such that every minimal right ideal is a right annihilator, its right socle is essential in R R, R is also indecomposable (as a ring), not simple, and R has no trivial idempotents. Then R is QF. In this case, QF-rings are the same as q−, f q−, a−, f a-rings. We also obtain that a right module (X, Y, f,) over a formal matrix ring R M N S with canonical isomorphisms f and g is automorphism-invariant if and only if X is an automorphism-invariant right R-module and Y is an automorphism-invariant right S-module.
DOI : 10.2298/FIL2329961T
Classification : 16D50, 16D70, 16D80, 16S50
Keywords: Automorphism-invariant module, f a-ring, Finite Goldie dimension, Formal matrix ring 
Le Van Thuyet; Truong Cong Quynh. On the automorphism-invariance of finitely generated ideals and formal matrix rings. Filomat, Tome 37 (2023) no. 29, p. 9961 . doi: 10.2298/FIL2329961T
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     title = {On the automorphism-invariance of finitely generated ideals and formal matrix rings},
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     year = {2023},
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     doi = {10.2298/FIL2329961T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2329961T/}
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