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Q:
Maximal Ideal in Dedekind Domain
Let $R$ be a Dedekind domain. What is the maximal ideal of $R$?
My main problem is that I don’t know the definition of maximal ideal. What I know is that it is prime ideal. But I don’t know what is the difference between a maximal ideal and a prime ideal. Can someone help me?
A:
A non-zero ideal $I$ of a Dedekind domain is maximal if and only if $I$ is prime. In fact every ideal is maximal if and only if $I$ is prime.
The maximal ideals are precisely the prime ideals.
Punk rockers Rise Against have announced a new album, titled «Endgame,» due out on March 17 via Rise Against Records. The disc is the first full-length album from the Chicago trio in three years, following 2012’s «The Sufferer & The Martyr.» The band’s previous record, «Give Up The Ghost,» was released in 2008.
The group spent the last several years recording the new album with producer Nick Launay (Suede, The Charlatans, Modest Mouse, Editors) in Los Angeles. The album features guest contributions from Declan McKenna (My Chemical Romance, The Killers), drummer Chris Kellogg (Sunn O))), bassist Jason Baez (The Thermals) and guitarist Ali Koehler (Converge, The Blood Brothers).
«Endgame» features the singles «The Church In Ruins,» «A Kind of Threat,» «In Plain Sight,» «The Undoing,» «Blessed Are The Meek,» «No Matter What» and «Run for Cover.»
Here is the tracklist:
1. The Church In Ruins
2. A Kind of Threat
3. In Plain Sight
4. The Undoing
5. Blesseds Are The Meek
6. No Matter What
7. Run for Cover
8. Every Time I Fall
9. Broken WingsCherry Grove, Missouri
Cherry Grove is a city in Clay County, Missouri, United States. The population
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