Natural Sciences, Mathematics, 2026
Completely generalized right primary rings and their extensions
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Submitted: 2024-12-17
© 2026 by author(s) and The Gufo Inc.
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Abstract
A ring RR is said to be a completely generalized right primary ring (c.g.r.pc.g.r.p ring) if a,b∈Ra,b∈R with ab=0ab=0 implies that a=0a=0 or bb is nilpotent. Let now RR be a ring and σσ an automorphism of RR. In this paper we extend the property of a completely generalized right primary ring (c.g.r.pc.g.r.p ring) to the skew polynomial ring R[x;σ]R[x;σ].