Geodesic
ON WEAKLY RIGID RINGS
Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 425-440

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a ring with a monomorphism α and an α-derivation δ. We introduce (α, δ)-weakly rigid rings which are a generalisation of α-rigid rings and investigate their properties. Every prime ring R is (α, δ)-weakly rigid for any automorphism α and α-derivation δ. It is proved that for any n, a ring R is (α, δ)-weakly rigid if and only if the n-by-n upper triangular matrix ring Tn(R) is (, )-weakly rigid if and only if Mn(R) is (, )-weakly rigid. Moreover, various classes of (α, δ)-weakly rigid rings is constructed, and several known results are extended. We show that for an (α, δ)-weakly rigid ring R, and the extensions R[x], R[[x]], R[x; α, δ], R[x, x−1; α], R[[x; α]], R[[x, x−1; α]], the ring R is quasi-Baer if and only if the extension over R is quasi-Baer. It is also proved that for an (α, δ)-weakly rigid ring R, if any one of the rings R, R[x], R[x; α, δ] and R[x, x−1; α] is left principally quasi-Baer, then so are the other three. Examples to illustrate and delimit the theory are provided.
DOI : 10.1017/S0017089509005084
Mots-clés : 16S36, 16W60 
NASR-ISFAHANI, A. R.; MOUSSAVI, A. ON WEAKLY RIGID RINGS. Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 425-440. doi: 10.1017/S0017089509005084
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509005084/}
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