Sums of semiprime, and ideals in a class of rings
Author:
Suzanne Larson
Journal:
Proc. Amer. Math. Soc. 109 (1990), 895901
MSC:
Primary 06F25; Secondary 13C13, 54C30
MathSciNet review:
1015682
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Abstract: In this paper it is shown that there is a large class of rings in which the sum of any two semiprime ideals is semiprime. This result is used to give a class of commutative rings with identity element in which the sum of any two ideals which are ideals is a ideal and the sum of any two ideals is a ideal.
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L. Gillman and C. Kohls, Convex and pseudoprime ideals in rings of continuous functions, Math. Z. 72 (1960), 399409. MR 0114115 (22:4942)
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M. Henriksen and F. A. Smith, Sums of ideals and semiprime ideals, Gen. Topology and its Relations to Modern Analysis and Algebra 5 (1982), 272278. MR 698424 (84d:54032)
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C. B. Huijsmans and B. de Pagter, On ideals and ideals in Riesz spaces I, Nederl. Akad. Wetensch. Indag. Math. 42 (1980), 183195. MR 577573 (81g:46010)
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, Ideal theory in algebras, Trans. Amer. Math. Soc. 269 (1982), 225245. MR 637036 (83k:06020)
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S. Larson, Pseudoprime ideals in a class of rings, Proc. Amer. Math. Soc. 104 (1988), 685692. MR 964843 (90a:06019)
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G. Mason, ideals and prime ideals, J. Algebra 26 (1973), 280297. MR 0321915 (48:280)
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, Prime ideals of and related rings, Canad. Math. Bull. 23 (1980), 437443. MR 602597 (82c:54013)
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D. Rudd, On two sum theorems for ideals of , Michigan Math. J. 17 (1970), 139141. MR 0259616 (41:4252)
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H. Subramanian, prime ideals in rings, Bull. Soc. Math. France 95 (1967), 193203. MR 0223284 (36:6332)
 [1]
 A. Bigard, K. Keimel, and S. Wolfenstein, Groupes et anneaux reficules, Lecture Notes in Math., vol. 608, SpringerVerlag, New York, 1977. MR 0552653 (58:27688)
 [2]
 L. Gillman and M. Jerison, Rings of continuous functions, SpringerVerlag, New York, 1960. MR 0116199 (22:6994)
 [3]
 L. Gillman and C. Kohls, Convex and pseudoprime ideals in rings of continuous functions, Math. Z. 72 (1960), 399409. MR 0114115 (22:4942)
 [4]
 M. Henriksen, Semiprime ideals of rings, Sympos. Math. 21 (1977), 401409. MR 0480256 (58:435)
 [5]
 M. Henriksen and F. A. Smith, Sums of ideals and semiprime ideals, Gen. Topology and its Relations to Modern Analysis and Algebra 5 (1982), 272278. MR 698424 (84d:54032)
 [6]
 C. B. Huijsmans and B. de Pagter, On ideals and ideals in Riesz spaces I, Nederl. Akad. Wetensch. Indag. Math. 42 (1980), 183195. MR 577573 (81g:46010)
 [7]
 , Ideal theory in algebras, Trans. Amer. Math. Soc. 269 (1982), 225245. MR 637036 (83k:06020)
 [8]
 S. Larson, Pseudoprime ideals in a class of rings, Proc. Amer. Math. Soc. 104 (1988), 685692. MR 964843 (90a:06019)
 [9]
 G. Mason, ideals and prime ideals, J. Algebra 26 (1973), 280297. MR 0321915 (48:280)
 [10]
 , Prime ideals of and related rings, Canad. Math. Bull. 23 (1980), 437443. MR 602597 (82c:54013)
 [11]
 D. Rudd, On two sum theorems for ideals of , Michigan Math. J. 17 (1970), 139141. MR 0259616 (41:4252)
 [12]
 H. Subramanian, prime ideals in rings, Bull. Soc. Math. France 95 (1967), 193203. MR 0223284 (36:6332)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199010156827
PII:
S 00029939(1990)10156827
Article copyright:
© Copyright 1990
American Mathematical Society
