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By Robert B. Warfield Jr. (auth.), David M. Arnold, Roger H. Hunter, Elbert A. Walker (eds.)

ISBN-10: 3540084479

ISBN-13: 9783540084471

ISBN-10: 3540370692

ISBN-13: 9783540370697

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Read or Download Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976 PDF

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Extra info for Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976

Example text

Suppose x I e (M;p) (A). Let v = M . p zero integers and a i ~ ( v * A ~ M ( A ) ) U M * ( A ) , Write x I = Zriai, where r. are nonx the generating set of (M;p)*(A). Since X is a decomposition basis, there is an integer s such that sria i is in [X] for all i. If we write sria i = ZjcitijY j, then sy I = ZieitilY I. Then there is at least one non-zero til for which the p-factor of s is equal to the p-factor of til. For this i, we have Hp(Sy I) ~ H p ( s r i a i) ~ ( t i l Y so a i ~ v*A~M(A). I) = Hp(SYl), But H(sy I) ~ H(sria i) ~ H(tilYl), implies H(ai) is compatible with M.

P. Crawley and A. W. Hales, The structure of Abelian p-groups by certain presentations, J. AIg. 12 (1969), 10-23. 12. E. G. , Krull-Schmidt and cancellation Pacific J. , 46 (1973), 115-121. in direct given over local rings, 36 13. L. Fuchs, Notes on Abelian groups, II, Acta Math. Acad. Sci. Hungar. Ii~(1960), 117-125. 14. L. , 75 (1971), 198-204. 15. L. Fuchs, Infinite Abelian Groups. vol. II, Academic Press, New York, 1973. 16. K. ~R. Goodearl, Power cancellation of groups and modules, Pacific J.

Krull-Schmidt and cancellation Pacific J. , 46 (1973), 115-121. in direct given over local rings, 36 13. L. Fuchs, Notes on Abelian groups, II, Acta Math. Acad. Sci. Hungar. Ii~(1960), 117-125. 14. L. , 75 (1971), 198-204. 15. L. Fuchs, Infinite Abelian Groups. vol. II, Academic Press, New York, 1973. 16. K. ~R. Goodearl, Power cancellation of groups and modules, Pacific J. Math. 64 i(1976), 387-411~ 17. P. Griffith, A solution to the splitting mixed group problem of Baer, Trans. Amer. Math. , 139 (1969), 261-269.

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Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976 by Robert B. Warfield Jr. (auth.), David M. Arnold, Roger H. Hunter, Elbert A. Walker (eds.)


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