A new class of simple noetherian V-domains

• Published in: Journal of algebra Vol. 493; pp. 410 - 437
• Main Authors: Ánh, P.N., van den Berg, J.E.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-01-2018
• Subjects: Hereditary torsion theory; PCI-ring; Simple noetherian domain; Twisted Laurent polynomial; V-domain; secondary; Twisted Laurent polynomial; Hereditary torsion theory; PCI-ring; Simple noetherian domain; V-domain; primary
• ISSN: 0021-8693; 1090-266X
• DOI: 10.1016/j.jalgebra.2017.09.032

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).