Abstract
A proper ideal P of a ring R is called
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prime if for each two ideals I, J in R the inclusion I ° J ⊆ P implies I ⊆ P or J ⊆ P; semiprime if it is an intersection of prime ideals.
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In a ring with identity every maximal ideal is prime.
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© 1998 Springer Science+Business Media Dordrecht
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Cǎlugǎreanu, G., Hamburg, P. (1998). Prime Ideals, Local Rings. In: Exercises in Basic Ring Theory. Kluwer Texts in the Mathematical Sciences, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9004-4_13
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DOI: https://doi.org/10.1007/978-94-015-9004-4_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4985-8
Online ISBN: 978-94-015-9004-4
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