Warfield Duality and Rank-one Quasi-summands of Tensor Products of Finite Rank Locally Free Modules over Dedekind Domains

(Journal of Algebra, 121(1989), pp. 129 - 138)

I love this little paper (well, 10 printed pages). As we all know, mathematics is a young wo/man's game, but as far as I personally am concerned this paper, written when I was almost fifty, can hold its own with any of the ones that established my reputation when I was younger. The main result is dramatically surprising, so much so that I think I must have been crazy to have ever dared to believe that such a thing might be true. And the proof uses very simple principles.

What I especially like is that what the proof uses is mostly a bunch of natural isomorphisms which are common currency in ring theory, but not much used by abelian group theorists.

Here's a brief quote from the referees report. ``This paper is a significant step in the author's almost single-handed investigation of tensor products of finite rank torsion-free modules over Dedekind domains.... It was a distinct pleasure to read this elegant paper. The author repeatedly demonstrates that, with a careful choice of words, complicated concepts can be expressed simply and understandably. Unfortunately, his penchant for brevity does not extend to the title, e.g. something like `Tensor products of locally free modules over Dedekind domains' would be less informative but also less overwhelming.''