A new class of simple noetherian V-domains

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).