Pseudoprime ideals in a class of rings
Author:
Suzanne Larson
Journal:
Proc. Amer. Math. Soc. 104 (1988), 685692
MSC:
Primary 06F25; Secondary 16A12
MathSciNet review:
964843
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: In a commutative ring, an ideal is called pseudoprime if implies or , and is called square dominated if for every for some such that . Several characterizations of pseudoprime ideals are given in the class of commutative semiprime rings in which minimal prime ideals are square dominated. It is shown that the hypothesis imposed on the rings, that minimal prime ideals are square dominated, cannot be omitted or generalized.
 [1]
Eleanor
R. Aron and Anthony
W. Hager, Convex vector lattices and 𝑙algebras,
Topology Appl. 12 (1981), no. 1, 1–10. MR 600458
(82c:54010), http://dx.doi.org/10.1016/01668641(81)900249
 [2]
Alain
Bigard, Klaus
Keimel, and Samuel
Wolfenstein, Groupes et anneaux réticulés,
Lecture Notes in Mathematics, Vol. 608, SpringerVerlag, BerlinNew York,
1977 (French). MR 0552653
(58 #27688)
 [3]
Leonard
Gillman and Meyer
Jerison, Rings of continuous functions, The University Series
in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton,
N.J.TorontoLondonNew York, 1960. MR 0116199
(22 #6994)
 [4]
Leonard
Gillman and Carl
W. Kohls, Convex and pseudoprime ideals in rings of continuous
functions, Math. Z. 72 (1959/1960), 399–409. MR 0114115
(22 #4942)
 [5]
Melvin
Henriksen, Semiprime ideals of 𝑓rings, Symposia
Mathematica, Vol. XXI (Convegno sulle Misure su Gruppi e su Spazi
Vettoriali, Convegno sui Gruppi e Anelli Ordinati, INDAM, Rome, 1975),
Academic Press, London, 1977, pp. 401–409. MR 0480256
(58 #435)
 [6]
M.
Henriksen and F.
A. Smith, Sums of 𝑧ideals and semiprime ideals,
General topology and its relations to modern analysis and algebra, V
(Prague, 1981) Sigma Ser. Pure Math., vol. 3, Heldermann, Berlin,
1983, pp. 272–278. MR 698424
(84d:54032)
 [7]
C.
B. Huijsmans, Some analogies between commutative rings, Riesz
spaces and distributive lattices with smallest element, Nederl. Akad.
Wetensch. Proc. Ser. A 77=Indag. Math. 36 (1974),
132–147. MR 0354635
(50 #7113)
 [8]
C.
B. Huijsmans and B.
de Pagter, Ideal theory in
𝑓algebras, Trans. Amer. Math. Soc.
269 (1982), no. 1,
225–245. MR
637036 (83k:06020), http://dx.doi.org/10.1090/S00029947198206370365
 [9]
Suzanne
Larson, Minimal convex extensions and intersections of primary
𝐼ideals in 𝑓rings, J. Algebra 123
(1989), no. 1, 99–110. MR 1000478
(90i:06023), http://dx.doi.org/10.1016/00218693(89)900379
 [10]
Gordon
Mason, 𝑧ideals and prime ideals, J. Algebra
26 (1973), 280–297. MR 0321915
(48 #280)
 [11]
H.
Subramanian, 𝑙prime ideals in 𝑓rings, Bull.
Soc. Math. France 95 (1967), 193–203. MR 0223284
(36 #6332)
 [1]
 E. Aron and A. Hager, Convex vector lattices and algebras, Topology Appl. 12 (1981), 110. MR 600458 (82c:54010)
 [2]
 A. Bigard, K. Keimel and S. Wolfenstein, Groups et anneaux reticules, Lecture Notes in Math., vol. 608, SpringerVerlag, 1977. MR 0552653 (58:27688)
 [3]
 L. Gillman and M. Jerison, Rings of continuous functions, SpringerVerlag, 1960. MR 0116199 (22:6994)
 [4]
 L. Gillman and C. Kohls, Convex and pseudoprime ideals in rings of continuous functions, Math. Z. 72 (1960), 399409. MR 0114115 (22:4942)
 [5]
 M. Henriksen, Semiprime ideals of rings, Sympos. Math. 21 (1977), 401409. MR 0480256 (58:435)
 [6]
 M. Henriksen and F. A. Smith, Sums of ideals and semiprime ideals, General Topology and Its Relations to Modern Analysis and Algebra 5 (1982), 272278. MR 698424 (84d:54032)
 [7]
 C. B. Huijsmans, Some analogies between commutative rings, Riesz spaces and distributive lattices with smallest element, Proc. Nederl. Akad. Wetensch. A77=Indag. Math. 36 (1974), 132147. MR 0354635 (50:7113)
 [8]
 C. B. Huijsmans and B. de Pagter, Ideal theory in algebras, Trans. Amer. Math. Soc. 269 (1982), 225245. MR 637036 (83k:06020)
 [9]
 S. Larson, Minimal convex extensions and intersections of primary ideals in rings, J. Algebra (to appear). MR 1000478 (90i:06023)
 [10]
 G. Mason, ideals and prime ideals, J. Algebra 26 (1973), 280297. MR 0321915 (48:280)
 [11]
 H. Subramanian, prime ideals in rings, Bull. Soc. Math. France 95 (1967), 193203. MR 0223284 (36:6332)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC:
06F25,
16A12
Retrieve articles in all journals
with MSC:
06F25,
16A12
Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198809648432
PII:
S 00029939(1988)09648432
Article copyright:
© Copyright 1988
American Mathematical Society
