Realization theorems for valuated p n -socles

Patrick W. Keef

Rendiconti del Seminario Matematico della Università di Padova (2011)

  • Volume: 126, page 151-173
  • ISSN: 0041-8994

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Keef, Patrick W.. "Realization theorems for valuated $p^n$ -socles." Rendiconti del Seminario Matematico della Università di Padova 126 (2011): 151-173. <http://eudml.org/doc/243162>.

@article{Keef2011,
author = {Keef, Patrick W.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Abelian -groups; valuated vector spaces; valuated -groups; -summable groups; Ulm functions},
language = {eng},
pages = {151-173},
publisher = {Seminario Matematico of the University of Padua},
title = {Realization theorems for valuated $p^n$ -socles},
url = {http://eudml.org/doc/243162},
volume = {126},
year = {2011},
}

TY - JOUR
AU - Keef, Patrick W.
TI - Realization theorems for valuated $p^n$ -socles
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2011
PB - Seminario Matematico of the University of Padua
VL - 126
SP - 151
EP - 173
LA - eng
KW - Abelian -groups; valuated vector spaces; valuated -groups; -summable groups; Ulm functions
UR - http://eudml.org/doc/243162
ER -

References

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  2. [2] P. Danchev - P. Keef, An application of set theory to ø + n -totally p ø + n -Projective primary abelian groups, Mediterr. J. Math. (to appear). Zbl1259.20059
  3. [3] P. Danchev - P. Keef, Generalized Wallace theorems, Math. Scand., 104 (1) (2009), pp. 33–50. Zbl1169.20029MR2498370
  4. [4] P. Danchev - P. Keef, n -Summable valuated p n -socles and primary abelian groups, Commun. Algebra, 38 (2010), pp. 3137–3153. Zbl1210.20049MR2724211
  5. [5] P. Danchev - P. Keef, Nice elongations of primary abelian groups, Publ. Mat., 54 (2) (2010), pp. 317–339. Zbl1214.20055MR2675926
  6. [6] L. Fuchs, Infinite Abelian Groups, Volumes I & II, Academic Press, (New York, 1970 and 1973). Zbl0257.20035
  7. [7] L. Fuchs, Vector spaces with valuations, J. Algebra, 35 (1975), pp. 23–38. Zbl0318.15002MR371995
  8. [8] P. Griffith, Infinite Abelian Group Theory, The University of Chicago Press (Chicago and London, 1970). Zbl0204.35001MR289638
  9. [9] K. Honda, Realism in the theory of abelian groups III, Comment. Math. Univ. St. Pauli, 12 (1964), pp. 75–111. Zbl0123.02302MR162848
  10. [10] R. Hunter - F. Richman - E. Walker, Existence Theorems for Warfield Groups, Trans. Amer. Math. Soc., 235 (1978), pp. 345–362. Zbl0368.20034MR473044
  11. [11] J. Irwin - P. Keef, Primary abelian groups and direct sums of cyclics, J. Algebra, 159 (2) (1993), pp. 387–399. Zbl0803.20035MR1231220
  12. [12] T. Jech, Set Theory (Third Millennium Edition), Springer (Berlin, 2002). Zbl1007.03002MR1940513
  13. [13] P. Keef, On ø 1 - p ø + n -projective primary abelian groups, J. Algebra and Number Theory Academia, 1 (1) (2010), pp. 53–87. Zbl1229.20055MR1222172
  14. [14] P. Keef - P. Danchev, On m , n -balanced projective and m , n -totally projective primary abelian groups, Submitted. Zbl1273.20053
  15. [15] P. Keef - P. Danchev, On n -simply presented primary abelian groups, To appear in Houston J. Math. Zbl1271.20066
  16. [16] F. Richman - E. Walker, Valuated groups, J. Algebra, 56 (1) (1979), pp. 145–167. Zbl0401.20049MR527162

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