Abstract:The author considers some properties of extension rings $B$ of a ring $A$ that satisfy the condition that every maximal ideal of $B$ is an extension of some ideal of $A$. Such extensions have been used by D. Lissner, K. Lønsted, N. Moore, and A. Simis to obtain rings for which the projective moduli are arbitrarily less than the dimension of the maximal spectra. It is shown that families of prime ideals of maximal type can be used to construct such extensions.
- Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
- Oscar Goldman, Determinants in projective modules, Nagoya Math. J. 18 (1961), 27–36. MR 124357 D. Lissner and K. Lønsted, Reduction of projective modulus in ring extensions (to appear).
- David Lissner and Nadine Moore, Projective modules over certain rings of quotients of affine rings, J. Algebra 15 (1970), 72–80. MR 257061, DOI 10.1016/0021-8693(70)90086-4
- Nadine Moore, Algebraic vector bundles over the $2$-sphere, Invent. Math. 14 (1971), 167–172. MR 294334, DOI 10.1007/BF01405362
- Aron Simis, Projective moduli and maximal spectra of certain quotient rings, Trans. Amer. Math. Soc. 170 (1972), 125–136. MR 319972, DOI 10.1090/S0002-9947-1972-0319972-6
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 37-41
- MSC: Primary 13C10; Secondary 13B99
- DOI: https://doi.org/10.1090/S0002-9939-1976-0435056-X
- MathSciNet review: 0435056