Abstract
AbstractTwo characterizations of semisimple classes of associative and alternative rings (and semigroups with 0) are given:(i) A class is a semisimple class if and only if it is hereditary, closed under extensions and subdirect sums;(ii) A class is a semisimple class if and only if it is hereditary, closed under extensions, and has the co-inductive property.The first characterization sharpens Armendariz's (1968) result proved for associative rings, the second one is categorically dual to a characterization of radical classes due to Amitsur (1954).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
