Projective moduli of certain quotient rings

Author:
Nadine Moore

Journal:
Proc. Amer. Math. Soc. **56** (1976), 37-41

MSC:
Primary 13C10; Secondary 13B99

MathSciNet review:
0435056

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Abstract: The author considers some properties of extension rings of a ring that satisfy the condition that every maximal ideal of is an extension of some ideal of . 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.

**[1]**Hyman Bass,*Algebraic 𝐾-theory*, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR**0249491****[2]**Oscar Goldman,*Determinants in projective modules*, Nagoya Math. J.**18**(1961), 27–36. MR**0124357****[3]**D. Lissner and K. Lønsted,*Reduction of projective modulus in ring extensions*(to appear).**[4]**David Lissner and Nadine Moore,*Projective modules over certain rings of quotients of affine rings.*, J. Algebra**15**(1970), 72–80. MR**0257061****[5]**Nadine Moore,*Algebraic vector bundles over the 2-sphere*, Invent. Math.**14**(1971), 167–172. MR**0294334****[6]**Aron Simis,*Projective moduli and maximal spectra of certain quotient rings*, Trans. Amer. Math. Soc.**170**(1972), 125–136. MR**0319972**, 10.1090/S0002-9947-1972-0319972-6

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DOI:
https://doi.org/10.1090/S0002-9939-1976-0435056-X

Keywords:
Projective modulus,
families of prime ideals of maximal type,
maximal spectrum,
unimodular element,
integral extension

Article copyright:
© Copyright 1976
American Mathematical Society