The dimension of the ring of coefficients in a polynomial ring

Author:
Jimmy T. Arnold

Journal:
Proc. Amer. Math. Soc. **49** (1975), 32-34

DOI:
https://doi.org/10.1090/S0002-9939-1975-0360553-4

MathSciNet review:
0360553

Full-text PDF

Abstract | References | Additional Information

Abstract: and are commutative rings with identity. We say that and are stably equivalent provided there exists a positive integer such that the polynomial rings and are isomorphic. If and are stably equivalent, then they have equal Krull dimension.

**[1]**S. Abhyankar, P. Eakin and W. Heinzer,*On the uniqueness of the coefficient ring in a polynomial ring*, J. Algebra**23**(1972), 310-342. MR**46**#5300. MR**0306173 (46:5300)****[2]**J. Brewer and E. Rutter,*Isomorphic polynomial rings*, Arch. Math.**23**(1972), 484-488. MR**0320068 (47:8609)****[3]**D. B. Coleman and E. E. Enochs,*Isomorphic polynomial rings*, Proc. Amer. Math. Soc.**27**(1971), 247-252. MR**42**#7686. MR**0272805 (42:7686)****[4]**P. Eakin and K. Kubota,*A note on the uniqueness of rings of coefficients in polynomial rings*, Proc. Amer. Math. Soc.**23**(1972), 333-341. MR**45**#6815. MR**0297763 (45:6815)****[5]**P. Eakin and W. Heinzer,*A cancellation problem for rings*, Proc. Conference on Commutative Algebra, Lecture Notes in Math., vol. 311, Springer-Verlag, Berlin and New York, 1973, pp. 61-77. MR**0349664 (50:2157)****[6]**M. Hochster,*Nonuniqueness of coefficient rings in a polynomial ring*, Proc. Amer. Math. Soc.**34**(1972), 81-82. MR**45**#3394. MR**0294325 (45:3394)****[7]**I. Kaplansky,*Commutative rings*, Allyn and Bacon, Boston, Mass., 1970. MR**40**#7234. MR**0254021 (40:7234)**

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0360553-4

Keywords:
Polynomial ring,
Krull dimension,
coefficient ring

Article copyright:
© Copyright 1975
American Mathematical Society