principal ideal


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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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These results on Euclidean self-dual cyclic codes have been generalized to abelian codes in group algebras [6] and the complete characterization and enumeration of Euclidean self-dual abelian codes in principal ideal group algebras (PIGAs) have been established.
Self-Dual Abelian Codes in Some Nonprincipal Ideal Group Algebras
Let 1 be the prime ideal of F' dividing l, and [lambda] an algebraic integer in F' generating the principal ideal 1.
Non-norm-euclidean fields in basic [Z.sub.l]-extensions
The principal ideal generated by 1 [direct sum] [epsilon] is a natural choice for our ideal I.
Tan's epsilon-determinant and ranks of matrices over semirings
In particular, [9] deals with the factorization of formal power series over principal ideal domains.
A factorization formula in Z[[[chi]]]
Since S is a semilattice, every principal ideal SsS has a unique generator s -[member of]S, so this order is well defined.
Morita invariants for partially ordered semigroups with local units/Lokaalsete uhikutega osaliselt jarjestatud poolruhmade Morita invariandid
0] is a principal ideal with countable infinite generators.
Substructures in algebras of associated homogeneous distributions on R
In [1], Campoli proved that Z[[theta]] is a principal ideal domain which is not a Euclidean domain.
Euclidean semimodules
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.
Basic quadratic forms
Since ker P is an ideal in C[z] and since every ideal in C[z] is a principal ideal (cf.
On one question of Ed Staff
Let I be a coherent ideal of [Mathematical Expression Omitted], that is a principal ideal generated by a function [Mathematical Expression Omitted].
On the rigidity of Bergman submodules
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.
Introduction to abstract algebra, 3d ed
Rather, we advocate patience and prudence as principal ideals for the road to recovery.
Patience paves way to recovery

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