Abstract
If R is any simple left noetherian, left hereditary, left V-domain, it is proven that the localization of R at any hereditary torsion theory τ that is cogenerated by a nonzero semisimple module, yields a ring of quotients Rτ with the same aforementioned properties. Examples of left V-domains R possessing (up to isomorphism) a single simple left R-module have been constructed by Cozzens (in 1970), and possessing infinitely many simple left R-modules, by Osofsky (in 1971). The methods developed in this paper can be used to construct V-domains possessing any prescribed number (finite or infinite) of simples. This answers in the affirmative a question posed by Cozzens and Faith in their book Simple Noetherian rings (Cambridge University Press, 1975).
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.
