TY - JOUR
T1 - The ascending chain condition on principal ideals in composite generalized power series rings
AU - Lim, Jung Wook
AU - Oh, Dong Yeol
N1 - Publisher Copyright:
© 2019 Rocky Mountain Mathematics Consortium.
PY - 2019
Y1 - 2019
N2 - Let D ⊆ E be an extension of commutative rings with identity, I a nonzero proper ideal of D, (γ;≤) a strictly totally ordered monoid such that 0 ≤αfor all α ∈ γ, and γ∗ = γ\ {0}. Let D+[Eγ∗, ≤] = {f 2 [Eγ;≤] f(0) ∈ D} and D+[Iγ∗, ≤] = {f ∈ [Dγ;≤] f(α) ∈ I for all α ∈ γ}. In this paper, we give some conditions for the rings D+[Eγ∗, ≤] and D +[Iγ∗, ≤] to satisfy the ascending chain condition on principal ideals.
AB - Let D ⊆ E be an extension of commutative rings with identity, I a nonzero proper ideal of D, (γ;≤) a strictly totally ordered monoid such that 0 ≤αfor all α ∈ γ, and γ∗ = γ\ {0}. Let D+[Eγ∗, ≤] = {f 2 [Eγ;≤] f(0) ∈ D} and D+[Iγ∗, ≤] = {f ∈ [Dγ;≤] f(α) ∈ I for all α ∈ γ}. In this paper, we give some conditions for the rings D+[Eγ∗, ≤] and D +[Iγ∗, ≤] to satisfy the ascending chain condition on principal ideals.
KW - Ascending chain condition on principal ideals
KW - Generalized power series rings
KW - Ring extensions
UR - https://www.scopus.com/pages/publications/85072667010
U2 - 10.1216/RMJ-2019-49-4-1223
DO - 10.1216/RMJ-2019-49-4-1223
M3 - Article
AN - SCOPUS:85072667010
SN - 0035-7596
VL - 49
SP - 1223
EP - 1236
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
IS - 4
ER -