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ON m, n-BALANCED PROJECTIVE AND m, n-TOTALLY PROJECTIVE PRIMARY ABELIAN GROUPS
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 Title & Authors
ON m, n-BALANCED PROJECTIVE AND m, n-TOTALLY PROJECTIVE PRIMARY ABELIAN GROUPS
Keef, Patrick W.; Danchev, Peter V.;
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 Abstract
If and are non-negative integers, then three new classes of abelian -groups are defined and studied: the , -simply presented groups, the , -balanced projective groups and the , -totally projective groups. These notions combine and generalize both the theories of simply presented groups and -projective groups. If , $n
 Keywords
abelian p-groups;m, n-simply presented groups;m, n-balanced projective groups;m, n-totally projective groups;summable groups;
 Language
English
 Cited by
1.
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ON ALMOST n-SIMPLY PRESENTED ABELIAN p-GROUPS, Korean Journal of Mathematics, 2013, 21, 4, 401  crossref(new windwow)
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On ω1-n-simply presented abelian p-groups, Journal of Algebra and Its Applications, 2015, 14, 03, 1550032  crossref(new windwow)
3.
On α-Simply Presented Abelian p-Groups, Mathematical Proceedings of the Royal Irish Academy, 2014, 114, 2, 1  crossref(new windwow)
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On variations of m,n-simply presented abelian p-groups, Science China Mathematics, 2014, 57, 9, 1771  crossref(new windwow)
 References
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. crossref(new window)

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. crossref(new window)

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. crossref(new window)

8.
P. Hill, The recovery of some abelian groups from their socles, Proc. Amer. Math. Soc. 86 (1982), no. 4, 553-560. crossref(new window)

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. crossref(new window)

12.
P. Keef, On the Tor functor and some classes of abelian groups, Pacific J. Math. 132 (1988), no. 1, 63-84. crossref(new window)

13.
P. Keef , On iterated torsion products of abelian p-groups, Rocky Mountain J. Math. 21 (1991), no. 3, 1035-1055. crossref(new window)

14.
P. Keef , Generalization of purity in primary abelian groups, J. Algebra 167 (1994), no. 2, 309-329. crossref(new window)

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. crossref(new window)

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. crossref(new window)

19.
R. Nunke, On the structure of Tor II, Pacific J. Math. 22 (1967), 453-464. crossref(new window)

20.
F. Richman and E. Walker, Valuated groups, J. Algebra 56 (1979), no. 1, 145-167. crossref(new window)