대한수학회지 (Journal of the Korean Mathematical Society)

  • 제50권2호
  • /
  • Pages.307-330
  • /
  • 2013
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON m, n-BALANCED PROJECTIVE AND m, n-TOTALLY PROJECTIVE PRIMARY ABELIAN GROUPS

  • Keef, Patrick W. (Department of Mathematics Whitman College) ;
  • Danchev, Peter V. (Department of Mathematics Plovdiv University "P. Hilendarski")
  • 투고 : 2012.01.12
  • 발행 : 2013.03.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

If $m$ and $n$ are non-negative integers, then three new classes of abelian $p$-groups are defined and studied: the $m$, $n$-simply presented groups, the $m$, $n$-balanced projective groups and the $m$, $n$-totally projective groups. These notions combine and generalize both the theories of simply presented groups and $p^{w+n}$-projective groups. If $m$, $n=0$, these all agree with the class of totally projective groups, but when $m+n{\geq}1$, they also include the $p^{w+m+n}$-projective groups. These classes are related to the (strongly) n-simply presented and (strongly) $n$-balanced projective groups considered in [15] and the n-summable groups considered in [2]. The groups in these classes whose lengths are less than ${\omega}^2$ are characterized, and if in addition we have $n=0$, they are determined by isometries of their $p^m$-socles.

키워드

참고문헌

  1. D. Cutler, Another summable C -group, Proc. Amer. Math. Soc. 26 (1970), 43-44.
  2. P. Danchev and P. Keef, n-summable valuated pn-socles and primary abelian groups, Comm. Algebra 38 (2010), no. 9, 3137-3153. https://doi.org/10.1080/00927870903164651
  3. L. Fuchs, Infinite Abelian Groups, Vol. I & II, Academic Press, New York, 1970 and 1973.
  4. L. Fuchs, Vector spaces with valuations, J. Algebra 35 (1975), 23-38. https://doi.org/10.1016/0021-8693(75)90033-2
  5. L. Fuchs, On $p^{w+n}$-projective abelian p-groups, Publ. Math. Debrecen 23 (1976), no. 3-4, 309-313.
  6. P. Griffith, Infinite Abelian Group Theory, The University of Chicago Press, Chicago and London, 1970.
  7. P. Hill, Criteria for total projectivity, Canad. J. Math. 33 (1981), 817-825. https://doi.org/10.4153/CJM-1981-063-x
  8. P. Hill, The recovery of some abelian groups from their socles, Proc. Amer. Math. Soc. 86 (1982), no. 4, 553-560. https://doi.org/10.1090/S0002-9939-1982-0674080-1
  9. P. Hill and C. Megibben, On direct sums of countable groups and generalizations, Studies on Abelian Groups (Symposium, Montpellier, 1967) pp. 183-206 Springer, Berlin, 1968.
  10. K. Honda, Realism in the theory of abelian groups III, Comment. Math. Univ. St. Pauli 12 (1964), 75-111.
  11. J. Irwin and P. Keef, Primary abelian groups and direct sums of cyclics, J. Algebra 159 (1993), no. 2, 387-399. https://doi.org/10.1006/jabr.1993.1163
  12. P. Keef, On the Tor functor and some classes of abelian groups, Pacific J. Math. 132 (1988), no. 1, 63-84. https://doi.org/10.2140/pjm.1988.132.63
  13. P. Keef , On iterated torsion products of abelian p-groups, Rocky Mountain J. Math. 21 (1991), no. 3, 1035-1055. https://doi.org/10.1216/rmjm/1181072928
  14. P. Keef , Generalization of purity in primary abelian groups, J. Algebra 167 (1994), no. 2, 309-329. https://doi.org/10.1006/jabr.1994.1187
  15. P. Keef and P. Danchev, On n-simply presented primary abelian groups, Houston J. Math. 38 (2012), no. 4, 1027-1050.
  16. C. Megibben, The generalized Kulikov criterion, Canad. J. Math. 21 (1969), 1192-1205. https://doi.org/10.4153/CJM-1969-132-9
  17. R. Nunke, Purity and subfunctors of the identity, Topics in Abelian Groups, Scott, 121-171, Foresman and Co., 1963.
  18. R. Nunke, Homology and direct sums of countable abelian groups, Math. Z. 101 (1967), no. 3, 182-212. https://doi.org/10.1007/BF01135839
  19. R. Nunke, On the structure of Tor II, Pacific J. Math. 22 (1967), 453-464. https://doi.org/10.2140/pjm.1967.22.453
  20. F. Richman and E. Walker, Valuated groups, J. Algebra 56 (1979), no. 1, 145-167. https://doi.org/10.1016/0021-8693(79)90330-2

피인용 문헌

  1. On ω1-n-simply presented abelian p-groups vol.14, pp.03, 2015, https://doi.org/10.1142/S0219498815500322
  2. On variations of m,n-simply presented abelian p-groups vol.57, pp.9, 2014, https://doi.org/10.1007/s11425-014-4822-2
  3. ON ALMOST n-SIMPLY PRESENTED ABELIAN p-GROUPS vol.21, pp.4, 2013, https://doi.org/10.11568/kjm.2013.21.4.401
  4. On α-simply presented abelian p-groups vol.114A, pp.2, 2014, https://doi.org/10.3318/pria.2014.114.13