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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Prime ideals and sheaf representation of a pseudo symmetric ring


Author: Gooyong Shin
Journal: Trans. Amer. Math. Soc. 184 (1973), 43-60
MSC: Primary 16A34
MathSciNet review: 0338058
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Abstract: Almost symmetric rings and pseudo symmetric rings are introduced. The classes of symmetric rings, of almost symmetric rings, and of pseudo symmetric rings are in a strictly increasing order. A sheaf representation is obtained for pseudo symmetric rings, similar to the cases of symmetric rings, semiprime rings, and strongly harmonic rings. Minimal prime ideals of a pseudo symmetric ring have the same characterization, due to J. Kist, as for the commutative case. A characterization is obtained for a pseudo symmetric ring with a certain right quotient ring to have compact minimal prime ideal space, extending a result due to Mewborn.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0338058-9
PII: S 0002-9947(1973)0338058-9
Keywords: Prime ideal, sheaf representation, pseudo symmetric ring, minimal prime ideal space
Article copyright: © Copyright 1973 American Mathematical Society