TY - JOUR
T1 - Pseudoprime L-Ideals in a Class of F-Rings
AU - Larson, Suzanne
N1 - pLarson, S. emPseudoprime L-Ideals in a Class of F-Rings,/em Proceedings of the American Mathematical Society. vol. 104 (1988) pp. 685-692./p
PY - 1988/11/1
Y1 - 1988/11/1
N2 - In a commutative f-ring, an l-ideal I is called pseudoprime if ab = 0 implies a ∈ I or b ∈ I, and is called square dominated if for every a ∈ I, |a| ≤ x 2 for some x ∈ A such that x 2 ∈ I. Several characterizations of pseudoprime l-ideals are given in the class of commutative semiprime f-rings in which minimal prime l-ideals are square dominated. It is shown that the hypothesis imposed on the f-rings, that minimal prime l-ideals are square dominated, cannot be omitted or generalized.
AB - In a commutative f-ring, an l-ideal I is called pseudoprime if ab = 0 implies a ∈ I or b ∈ I, and is called square dominated if for every a ∈ I, |a| ≤ x 2 for some x ∈ A such that x 2 ∈ I. Several characterizations of pseudoprime l-ideals are given in the class of commutative semiprime f-rings in which minimal prime l-ideals are square dominated. It is shown that the hypothesis imposed on the f-rings, that minimal prime l-ideals are square dominated, cannot be omitted or generalized.
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U2 - 10.1090/S0002-9939-1988-0964843-2
DO - 10.1090/S0002-9939-1988-0964843-2
M3 - Article
SN - 1088-6826
VL - 104
SP - 685
EP - 692
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 3
ER -