Modules over discrete valuation domains. III

P. A. Krylov; A. A. Tuganbaev

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Modules over discrete valuation domains. III

P. A. Krylov ; A. A. Tuganbaev

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 164 (2019), pp. 74-95.

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Résumé

This review paper is a continuation of two previous review papers devoted to properties of modules over discrete valuation domains. The first and second parts of this work (containing respectively of Chaps. 1–4, Secs. 1–22 and Chaps. 5–8, Secs. 23–39) were published in Journal of Mathematical Sciences (New York), 145, No. 4, 4997–5117 (2007), and 151, No. 5, 3225-3371 (2008). In this review paper, we continue the numeration of chapters and sections of parts I and II. The present third part consists of Chap. 9 “Appendix,” Secs. 40–42. In Sec. 40, we consider $p$-adic torsion-free modules with isomorphic automorphism groups. Section 41 is devoted to torsion-free modules over a complete discrete valuation domain with isomorphic radicals of their endomorphism rings. The volume of the paper does not allow us to provide proofs of all results that appeared after publication of the previous parts and directly related to the issues under consideration in it. In the final Section 42, we describe some of these new results.

Mots-clés : discrete valuation domain, $p$-adic module
Keywords: endomorphism ring.

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P. A. Krylov; A. A. Tuganbaev. Modules over discrete valuation domains. III. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 164 (2019), pp. 74-95. http://geodesic.mathdoc.fr/item/INTO_2019_164_a1/

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