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principal ideal

   Also found in: Wikipedia 0.01 sec.
principal ideal [′prin·sə·pəl ī′dēl]
(mathematics)
The smallest ideal of a ring which contains a given element of the ring.


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Using mainly concrete constructions, Gerstein gives a brief introduction to classical forms, then moves to quadratic spaces and lattices, valuations, local fields, p-adic numbers, quadratic spaces over Qp and over Q, lattices over principal ideal domains, initial integral results, the local-global approach to lattices, and applications to cryptography.
Rather, we advocate patience and prudence as principal ideals for the road to recovery.
This edition, which includes new sections on modules(free, semisimple and projective), modules over principal ideal domains, semidirect products, and the Wedderburn-Artin theorem also includes new appendices on Zorn's lemma and the proof of the recursive theorem.
 
 
 
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