Sums of semiprime, and -ideals in a class of -rings

Author:
Suzanne Larson

Journal:
Proc. Amer. Math. Soc. **109** (1990), 895-901

MSC:
Primary 06F25; Secondary 13C13, 54C30

DOI:
https://doi.org/10.1090/S0002-9939-1990-1015682-7

MathSciNet review:
1015682

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**A. Bigard, K. Keimel, and S. Wolfenstein,*Groupes et anneaux reficules*, Lecture Notes in Math., vol. 608, Springer-Verlag, New York, 1977. MR**0552653 (58:27688)****[2]**L. Gillman and M. Jerison,*Rings of continuous functions*, Springer-Verlag, 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), 399-409. MR**0114115 (22:4942)****[4]**M. Henriksen,*Semiprime ideals of**-rings*, Sympos. Math.**21**(1977), 401-409. 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), 272-278. 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), 183-195. MR**577573 (81g:46010)****[7]**-,*Ideal theory in**-algebras*, Trans. Amer. Math. Soc.**269**(1982), 225-245. MR**637036 (83k:06020)****[8]**S. Larson,*Pseudoprime**-ideals in a class of**-rings*, Proc. Amer. Math. Soc.**104**(1988), 685-692. MR**964843 (90a:06019)****[9]**G. Mason,*-ideals and prime ideals*, J. Algebra**26**(1973), 280-297. MR**0321915 (48:280)****[10]**-,*Prime**-ideals of**and related rings*, Canad. Math. Bull.**23**(1980), 437-443. MR**602597 (82c:54013)****[11]**D. Rudd,*On two sum theorems for ideals of*, Michigan Math. J.**17**(1970), 139-141. MR**0259616 (41:4252)****[12]**H. Subramanian,*-prime ideals in**-rings*, Bull. Soc. Math. France**95**(1967), 193-203. MR**0223284 (36:6332)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1015682-7

Article copyright:
© Copyright 1990
American Mathematical Society