Nilradicals of skew Hurwitz series of rings
AbstractFor a ring endomorphism α of a ring R, Krempa called α a rigid endomorphism if aα(a)=0 implies a = 0 for a in R. A ring R is called rigid if there exists a rigid endomorphism of R. In this paper, we extend the α-rigid property of a ring R to the upper nilradical N_r(R) of R. For an endomorphism α and the upper nilradical N_r(R) of a ring R, we introduce the condition (*): N_r(R) is a α-ideal of R and aα(a) in N_r(R) implies a in N_r(R) for a in R. We study characterizations of a ring R with an endomorphism α satisfying the condition (*), and we investigate their related properties. The connections between the upper nilradical of R and the upper nilradical of the skew Hurwitz series ring (HR,α) of R are also investigated.
The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.