Rocky Mountain Journal of Mathematics

Tensor products and endomorphism rings of finite valuated groups

Ulrich Albrecht

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Abstract

This paper discusses homological properties of a finite valuated $p$-group $A$. A category equivalence between full subcategories of the category of valuated $p$-groups and the category of right modules over the endomorphism ring of $A$ is developed to study $A$-presented and $A$-valuated valuated $p$-groups. In particular, we show that these classes do not coincide if $|A/pA| \gt p$. Examples are given throughout the paper.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 3 (2018), 703-727.

Dates
First available in Project Euclid: 2 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1533230821

Digital Object Identifier
doi:10.1216/RMJ-2018-48-3-703

Mathematical Reviews number (MathSciNet)
MR3835568

Zentralblatt MATH identifier
06917343

Subjects
Primary: 20K40: Homological and categorical methods
Secondary: 18G50: Nonabelian homological algebra 20K30: Automorphisms, homomorphisms, endomorphisms, etc.

Keywords
Valuated groups endomorphism rings preabelian categories

Citation

Albrecht, Ulrich. Tensor products and endomorphism rings of finite valuated groups. Rocky Mountain J. Math. 48 (2018), no. 3, 703--727. doi:10.1216/RMJ-2018-48-3-703. https://projecteuclid.org/euclid.rmjm/1533230821


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References

  • U. Albrecht, Bewertete $p$-Gruppen und ein Satz von Szele, J. Algebra 97 (1985), 201–220.
  • ––––, Faithful abelian groups of infinite rank, Proc. Amer. Math. Soc. 103 (1988), 21–26.
  • D.M. Arnold, Abelian groups and representations of finite partially ordered sets, CMS Books Mathematics, Springer, Berlin, 2000.
  • H. Bass, Finistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488.
  • L. Fuchs, Infinite Abelian groups, Volume I, Academic Press, New York, 1970.
  • ––––, Infinite Abelian groups, Volume II, Academic Press, New York, 1973.
  • R. Hunter, F. Richman and E.A. Walker, Simply presented valuated $p$-groups, J. Algebra 49 (1977), 125–133.
  • ––––, Finite direct sums of cyclic valuated $p$-groups, Pacific J. Math. 69 (1977), 97–133.
  • F. Richman and E.A. Walker, Ext in pre-abelian categories, Pacific J. Math. 71 (1977), 521–535.
  • ––––, Valuated groups, J. Algebra 56 (1979), 145–167.
  • J. Rotman, An introduction to homological algebra, Academic Press, New York, 1979.
  • P. Schultz, The endomorphism ring of a valuated group, Contemp. Math. 87 (1989), 75–84.
  • B. Stenstrom, Rings of quotients, Grundl. Math. Wissen. 217, Springer-Verlag, Heidelberg, 1975.
  • A.V. Yakolev, Homological algebra in pre-abelian categories, J. Soviet Math. 19 (1982), 1060–1067.