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.

Let 1 be the prime ideal of F' dividing l, and [lambda] an algebraic integer in F' generating the

principal ideal 1.

The

principal ideal generated by 1 [direct sum] [epsilon] is a natural choice for our ideal I.

In particular, [9] deals with the factorization of formal power series over

principal ideal domains.

Since S is a semilattice, every

principal ideal SsS has a unique generator s -[member of]S, so this order is well defined.

0] is a

principal ideal with countable infinite generators.

In [1], Campoli proved that Z[[theta]] is a

principal ideal domain which is not a Euclidean domain.

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.

Since ker P is an ideal in C[z] and since every ideal in C[z] is a

principal ideal (cf.

Let I be a coherent ideal of [Mathematical Expression Omitted], that is a

principal ideal generated by a function [Mathematical Expression Omitted].

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.

Rather, we advocate patience and prudence as

principal ideals for the road to recovery.