Noninvertible retracts
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- by Joe Yanik PDF
- Proc. Amer. Math. Soc. 87 (1983), 29-32 Request permission
Abstract:
We demonstrate that if $P$ is a projective $R[X]$-module that is not stably extended from an $R$-module, then the symmetric algebra of $P$ over $R[X]$ is a retract of a polynomial ring over $R$, but is not an invertible $R$-algebra. Hence, there are noninvertible retracts over a quite general class of rings.References
- Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491 N. Bourbaki, Algebra. I, Hermann, Paris, 1970.
- E. H. Connell, A $K$-theory for the category of projective algebras, J. Pure Appl. Algebra 5 (1974), 281–292. MR 384803, DOI 10.1016/0022-4049(74)90038-3
- Paul Eakin and William Heinzer, A cancellation problem for rings, Conference on Commutative Algebra (Univ. Kansas, Lawrence, Kan., 1972), Lecture Notes in Math., Vol. 311, Springer, Berlin, 1973, pp. 61–77. MR 0349664
- Cornelius Greither, Seminormality, projective algebras, and invertible algebras, J. Algebra 70 (1981), no. 2, 316–338. MR 623811, DOI 10.1016/0021-8693(81)90221-0
- Hideyuki Matsumura, Commutative algebra, 2nd ed., Mathematics Lecture Note Series, vol. 56, Benjamin/Cummings Publishing Co., Inc., Reading, Mass., 1980. MR 575344
- Charles A. Weibel, $K$-theory and analytic isomorphisms, Invent. Math. 61 (1980), no. 2, 177–197. MR 590161, DOI 10.1007/BF01390120
- Joe Yanik, Projective algebras, J. Pure Appl. Algebra 21 (1981), no. 3, 339–358. MR 617139, DOI 10.1016/0022-4049(81)90022-0
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 29-32
- MSC: Primary 13F20; Secondary 13D15
- DOI: https://doi.org/10.1090/S0002-9939-1983-0677224-1
- MathSciNet review: 677224