1. UNIQUE FACTORIZATION AND BIRTH OF ALMOST PRIMES
- Author
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Pramod K. Sharma and Srikant M. Bhatwadekar
- Subjects
Discrete mathematics ,Algebra and Number Theory ,Mathematics::Commutative Algebra ,Mathematics::Number Theory ,Semiprime ring ,Splitting of prime ideals in Galois extensions ,Associated prime ,Combinatorics ,Boolean prime ideal theorem ,Fractional ideal ,Unique prime ,Ascending chain condition on principal ideals ,Going up and going down ,Mathematics - Abstract
In studying unique factorization of domains we encountered a property of ideals. Using that we define the notion of almost prime ideals and prove that in Noetherian domains almost prime ideals are primary. We also prove that in a regular domain almost primes are precisely primes. Further, we define strictly nonprime ideals and study some inter relations between almost prime ideals, strictly nonprime ideals and factorization of ideals. more...
- Published
- 2005
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