ACCP in polynomial rings: a counterexample

ACCP in polynomial rings: a counterexample
HTML articles powered by AMS MathViewer

by William J. Heinzer and David C. Lantz PDF

Proc. Amer. Math. Soc. 121 (1994), 975-977 Request permission

We describe an example showing that ACCP need not extend from a ring to a polynomial ring over it.

References

D. D. Anderson, David F. Anderson, and Muhammad Zafrullah, Factorization in integral domains, J. Pure Appl. Algebra 69 (1990), no. 1, 1–19. MR 1082441, DOI 10.1016/0022-4049(90)90074-R
Maria Elisa Antunes Simões and Anne-Marie Nicolas, Exemples d’anneaux $n$-acc, Comm. Algebra 12 (1984), no. 13-14, 1653–1665 (French). MR 743309, DOI 10.1080/00927878408823072
Robert Gilmer, Multiplicative ideal theory, Pure and Applied Mathematics, No. 12, Marcel Dekker, Inc., New York, 1972. MR 0427289
Anne Grams, Atomic rings and the ascending chain condition for principal ideals, Proc. Cambridge Philos. Soc. 75 (1974), 321–329. MR 340249, DOI 10.1017/s0305004100048532
William Heinzer and David Lantz, Commutative rings with acc on $n$-generated ideals, J. Algebra 80 (1983), no. 1, 261–278. MR 690717, DOI 10.1016/0021-8693(83)90031-5

Thèse — modules factorables, modules n-acc

G. Renault, Sur des conditions de chaînes ascendantes dans des modules libres, J. Algebra 47 (1977), no. 2, 268–275 (French). MR 466116, DOI 10.1016/0021-8693(77)90225-3