ACCP rises to the polynomial ring if the ring has only finitely many associated primes

Frohn D (2004)
COMMUNICATIONS IN ALGEBRA 32(3): 1213-1218.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We show for a commutative ring R with unity: If R satisfies the ascending chain condition on principal ideals (accp) and has only finitely many associated primes, then for any set of indeterminates X the polynomial ring R[X] also satisfies accp. Further we show that accp rises to the power series ring R[[X]] if R satisfies accp and the ascending chain condition on annihilators.
Stichworte
polynomial ring; commutative ring; ascending chain condition; principal ideal
Erscheinungsjahr
2004
Zeitschriftentitel
COMMUNICATIONS IN ALGEBRA
Band
32
Ausgabe
3
Seite(n)
1213-1218
ISSN
0092-7872
eISSN
1532-4125
Page URI
https://pub.uni-bielefeld.de/record/1608390

Zitieren

Frohn D. ACCP rises to the polynomial ring if the ring has only finitely many associated primes. COMMUNICATIONS IN ALGEBRA. 2004;32(3):1213-1218.
Frohn, D. (2004). ACCP rises to the polynomial ring if the ring has only finitely many associated primes. COMMUNICATIONS IN ALGEBRA, 32(3), 1213-1218. doi:10.1081/AGB-120027975
Frohn, D. (2004). ACCP rises to the polynomial ring if the ring has only finitely many associated primes. COMMUNICATIONS IN ALGEBRA 32, 1213-1218.
Frohn, D., 2004. ACCP rises to the polynomial ring if the ring has only finitely many associated primes. COMMUNICATIONS IN ALGEBRA, 32(3), p 1213-1218.
D. Frohn, “ACCP rises to the polynomial ring if the ring has only finitely many associated primes”, COMMUNICATIONS IN ALGEBRA, vol. 32, 2004, pp. 1213-1218.
Frohn, D.: ACCP rises to the polynomial ring if the ring has only finitely many associated primes. COMMUNICATIONS IN ALGEBRA. 32, 1213-1218 (2004).
Frohn, Daniel. “ACCP rises to the polynomial ring if the ring has only finitely many associated primes”. COMMUNICATIONS IN ALGEBRA 32.3 (2004): 1213-1218.