## Certain overrings of right hereditary, right Noetherian rings are $V$-rings

HTML articles powered by AMS MathViewer

- by Friedhelm Hansen
- Proc. Amer. Math. Soc.
**52**(1975), 85-90 - DOI: https://doi.org/10.1090/S0002-9939-1975-0376764-8
- PDF | Request permission

## Abstract:

It will be shown that a particular quotient ring of a ring $R$ is a nontrivial $V$-ring if $R$ is a special kind of a right hereditary, right Noetherian ring. Another result states that all overrings of a right and left Goldie $V$-ring, which is semiartinian modulo every essential right ideal, are $V$-rings.## References

- H.-H. Brungs,
*Overrings of principal ideal domains*, Proc. Amer. Math. Soc.**28**(1971), 44–46. MR**271137**, DOI 10.1090/S0002-9939-1971-0271137-7 - A. W. Chatters,
*The restricted minimum condition in Noetherian hereditary rings*, J. London Math. Soc. (2)**4**(1971), 83–87. MR**292877**, DOI 10.1112/jlms/s2-4.1.83 - John H. Cozzens,
*Homological properties of the ring of differential polynomials*, Bull. Amer. Math. Soc.**76**(1970), 75–79. MR**258886**, DOI 10.1090/S0002-9904-1970-12370-9 - Carl Faith,
*Lectures on injective modules and quotient rings*, Lecture Notes in Mathematics, No. 49, Springer-Verlag, Berlin-New York, 1967. MR**0227206**, DOI 10.1007/BFb0074319 - Carl Faith,
*Algebra: rings, modules and categories. I*, Die Grundlehren der mathematischen Wissenschaften, Band 190, Springer-Verlag, New York-Heidelberg, 1973. MR**0366960**, DOI 10.1007/978-3-642-80634-6 - A. W. Goldie,
*Semi-prime rings with maximum condition*, Proc. London Math. Soc. (3)**10**(1960), 201–220. MR**111766**, DOI 10.1112/plms/s3-10.1.201 - Oscar Goldman,
*Rings and modules of quotients*, J. Algebra**13**(1969), 10–47. MR**245608**, DOI 10.1016/0021-8693(69)90004-0 - F. Hansen,
*On one-sided prime ideals*, Pacific J. Math.**58**(1975), no. 1, 79–85. MR**379582**, DOI 10.2140/pjm.1975.58.79 - Lawrence Levy,
*Unique subdirect sums of prime rings*, Trans. Amer. Math. Soc.**106**(1963), 64–76. MR**142567**, DOI 10.1090/S0002-9947-1963-0142567-9 - G. O. Michler and O. E. Villamayor,
*On rings whose simple modules are injective*, J. Algebra**25**(1973), 185–201. MR**316505**, DOI 10.1016/0021-8693(73)90088-4 - B. L. Osofsky,
*On twisted polynomial rings*, J. Algebra**18**(1971), 597–607. MR**280521**, DOI 10.1016/0021-8693(71)90142-6 - V. S. Ramamurthi and K. M. Rangaswamy,
*Generalized $V$-rings*, Math. Scand.**31**(1972), 69–77. MR**321974**, DOI 10.7146/math.scand.a-11412 - Bo Stenström,
*Rings and modules of quotients*, Lecture Notes in Mathematics, Vol. 237, Springer-Verlag, Berlin-New York, 1971. MR**0325663**, DOI 10.1007/BFb0059904

## Bibliographic Information

- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**52**(1975), 85-90 - MSC: Primary 16A52
- DOI: https://doi.org/10.1090/S0002-9939-1975-0376764-8
- MathSciNet review: 0376764