Projective modules over rings with many units

Authors:
B. R. McDonald and William C. Waterhouse

Journal:
Proc. Amer. Math. Soc. **83** (1981), 455-458

MSC:
Primary 13C10; Secondary 13B25

DOI:
https://doi.org/10.1090/S0002-9939-1981-0627668-7

MathSciNet review:
627668

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a commutative ring. Assume that every polynomial whose values generate the unit ideal actually takes on an invertible value. Then projective -modules split into cyclic summands, and those of constant rank are free.

**[1]**N. Bourbaki,*Algèbre commutative*, Chapters I, II, Hermann, Paris, 1961. MR**0171800 (30:2027)****[2]**K. R. Goodearl and R. B. Warfield, Jr.,*Algebras over zero-dimensional rings*, Math. Ann.**223**(1976), 157-168. MR**0412230 (54:357)****[3]**W. van der Kallen,*The**of rings with many units*, Ann. Sci. École Norm. Sup. (4)**10**(1977), 473-515. MR**0506170 (58:22018)****[4]**B. R. McDonald,*of rings with many units*, Comm. Algebra**8**(1980), 869-888. MR**571047 (81k:20068)****[5]**-,*Projectivities over rings with many units*, Comm. Algebra**9**(1981), 195-204. MR**600014 (82g:16037)****[6]**-,*for rings with many units*, Comm. Algebra**9**(1981), 205-220. MR**600015 (82m:20051)****[7]**W. C. Waterhouse,*Automorphisms of*, Proc. Amer. Math. Soc. 79 (1980), 347-351. MR**567969 (81h:20055)**

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DOI:
https://doi.org/10.1090/S0002-9939-1981-0627668-7

Article copyright:
© Copyright 1981
American Mathematical Society