Tag Archives: invertible ideals

Commutative Algebra 46

Posted on May 4, 2020 by limsup

Properties of Dedekind Domains Throughout this article, A denotes a Dedekind domain. Proposition 1. Every fractional ideal of A can be written as where each is a maximal ideal. The expression is unique up to permutation of terms. Note In … Continue reading →

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Commutative Algebra 45

Posted on May 3, 2020 by limsup

Invertibility is Local In this article, we again let A be an integral domain and K its field of fractions. We continue our discussion of invertible fractional ideals of A. Proposition 1. A fractional ideal M of A is invertible if and … Continue reading →

Posted in Advanced Algebra | Tagged , , , , , , | 7 Comments

Commutative Algebra 44

Posted on May 2, 2020 by limsup

Fractional Ideals Throughout this article, let A be an integral domain and K its field of fractions. We do not assume the ring to be noetherian. The objective here is to develop the theory of multiplying and dividing certain classes of non-zero … Continue reading →

Posted in Advanced Algebra | Tagged , , , , , | 5 Comments