Representation Type of Posets and Finite Rank Butler Groups

D. Arnold; M. Dugas

Colloquium Mathematicae (1998)

  • Volume: 74, Issue: 2, page 299-320
  • ISSN: 0010-1354

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Arnold, D., and Dugas, M.. "Representation Type of Posets and Finite Rank Butler Groups." Colloquium Mathematicae 74.2 (1998): 299-320. <http://eudml.org/doc/210520>.

@article{Arnold1998,
author = {Arnold, D., Dugas, M.},
journal = {Colloquium Mathematicae},
keywords = {finite rank Butler groups; representation type; representation theory of posets; category equivalences; wildness},
language = {eng},
number = {2},
pages = {299-320},
title = {Representation Type of Posets and Finite Rank Butler Groups},
url = {http://eudml.org/doc/210520},
volume = {74},
year = {1998},
}

TY - JOUR
AU - Arnold, D.
AU - Dugas, M.
TI - Representation Type of Posets and Finite Rank Butler Groups
JO - Colloquium Mathematicae
PY - 1998
VL - 74
IS - 2
SP - 299
EP - 320
LA - eng
KW - finite rank Butler groups; representation type; representation theory of posets; category equivalences; wildness
UR - http://eudml.org/doc/210520
ER -

References

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  1. D. M. Arnold, Finite Rank Torsion-Free Abelian Groups and Rings, Lecture Notes in Math. 931, Springer, New York, 1982. Zbl0493.20034
  2. D. M. Arnold, Representations of partially ordered sets and abelian groups, in: Contemp. Math. 87, Amer. Math. Soc., 1989, 91-109. 
  3. D. M. Arnold and M. Dugas, Block rigid almost completely decomposable groups and lattices over multiple pullback rings, J. Pure Appl. Algebra 87 (1993), 105-121. Zbl0818.20065
  4. D. M. Arnold and M. Dugas, Butler groups with finite typesets and free groups with distinguished subgroups, Comm. Algebra 21 (1993), 1947-1982. Zbl0776.20017
  5. D. M. Arnold and M. Dugas, Locally free finite rank Butler groups and near isomorphism, in: Abelian Groups and Modules, Kluwer, Boston, 1995, 41-48. Zbl0841.20051
  6. D. M. Arnold and M. Dugas, Representations of finite posets and near-isomorphism of finite rank Butler groups, Rocky Mountain J. Math. 25 (1995), 591-609. Zbl0835.20073
  7. D. M. Arnold and C. Vinsonhaler, Finite rank Butler groups: A survey of recent results, in: Abelian Groups, Lecture Notes in Pure and Appl. Math. 146, Marcel Dekker, New York, 1993, 17-41. Zbl0804.20043
  8. S. Brenner, Decomposition properties of some small diagrams of modules, Sympos. Math. 13 (1974), 127-141. 
  9. M. C. R. Butler, A class of torsion-free abelian groups of finite rank, Proc. London Math. Soc. (3) 15 (1965), 680-698. Zbl0131.02501
  10. M. C. R. Butler, Torsion-free modules and diagrams of vector spaces, ibid. 18 (1968), 635-652. Zbl0179.32603
  11. M. C. R. Butler, Some almost split sequences in torsion-free abelian group theory, in: Abelian Group Theory, Gordon and Breach, New York, 1987, 291-302. 
  12. M. Dugas and E. Oxford, Near isomorphism invariants for a class of almost completely decomposable groups, in: Abelian Groups, Lecture Notes in Pure and Appl. Math. 146, Marcel Dekker, New York, 1993, 129-150. Zbl0806.20042
  13. S. Files and R. Goebel, Gauß' theorem for two submodules, submitted for publication, 1996. 
  14. L. Fuchs, Infinite Abelian Groups, Vol. II, Academic Press, New York, 1973. Zbl0257.20035
  15. E. L. Lady, Nearly isomorphic torsion-free abelian groups, J. Algebra 35 (1975), 235-238. Zbl0322.20025
  16. V. V. Plahotnik, Representations of partially ordered sets over commutative rings, Math. USSR-Izv. 10 (1976), 497-514. Zbl0369.06002
  17. F. Richman, Isomorphism of Butler groups at a prime, in: Abelian Group Theory and Related Topics (Oberwolfach, 1993), Contemp. Math. 171, 1994, 333-337. Zbl0857.20035
  18. D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Gordon and Breach, Philadelphia, 1992. Zbl0818.16009
  19. D. Simson, On representation types of module subcategories and orders, Bull. Polish Acad. Sci. Math. 41 (1993), 77-93. Zbl0805.16011
  20. D. Simson, Socle projective representations of partially ordered sets and Tits quadratic forms with applications to lattices over orders, in: Abelian Groups and Modules, Marcel Dekker, New York, 1996, 73-112. Zbl0869.16008

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